We consider a nonlinear profit maximization problem in the Lotka–McKendrick model of age-structured harvested population describing farmed populations in agriculture and aquaculture. The control functions are time- and age-dependent harvesting rate and time dependent supply of newborns. We establish the existence of optimal controls with measure-valued harvesting rate by using distributional partial

The Neumann boundary value problem for the Poisson equation is explicitly solved under a natural compatibility condition for the data in a particular planar circular rectangle. The case studied here is different from regular cases as the normalization condition for the Neumann function given as an integral is divergent. Hence, no normalization condition for the Neumann problem is available and the

We consider a swelling porous-elastic system with a single nonlinear damping in the elastic equation. Recently, Ramos et al. [Stability results for elastic porous media swelling with nonlinear damping. J Math Phys. 2020;61(10):101505.] considered the same system and established a general decay result provided that the wave speeds of the system are equal. In this paper, we obtain the general decay result

For the first time in this paper, the dual problem is constructed for the problem with generalized first order partial differential inclusions, the duality theorem is proved. For discrete problems, necessary and sufficient optimality conditions are derived in the form of the Euler–Lagrange type inclusion. Thus, it is possible to construct dual problems for problems with partial differential inclusions

In this paper, we establish sufficient conditions for the existence of solutions for a class of initial value problems for impulsive fractional differential equations involving the deformable fractional derivative. We achieve our results using classical fixed point theorems such as the Banach contraction principle, the Shaefer and the alternative Leray–Schauder theorems. We provide an example to illustrate

The investigation on the oscillatory and asymptotic properties of differential equations plays an important role in many applications, such as engineering, physics and medicine. In this work, we establish some new sufficient conditions for both the oscillatory and asymptotic behavior of the solutions to a second-order neutral impulsive differential system (IDS, for short) with deviating argument and

In this paper, a new concept of square-mean compact asymptotically almost automorphy for stochastic processes is introduced and a composition theorem is also proved. And then, this notion is applied to investigate existence and uniqueness theorems for squaremean compact asymptotically almost automorphic mild solutions to an abstract stochastic integro-differential equation with infinite delay. Moreover

In this paper, we consider a bilinear optimal control with final observation for the heat equation. We first give the existence and uniqueness results of weak solutions under an integral constraints on the control and the state. We prove the existence and uniqueness of the solution to a quadratic boundary optimal control problem by means of compactness Sobolev space embedding. Then we provide a characterization

In this paper, by using the concentration-compactness principle of Lions for variable exponents found in [Bonder JF, Silva A. Concentration-compactness principal for variable exponent space and applications. Electron J Differ Equ. 2010;141:1–18.] and the Mountain Pass Theorem without the Palais–Smale condition given in [Rabinowitz PH. Minimax Methods in Critical Point Theory with Applications to Differential

ABSTRACT In this paper, we are concerned with the following singular perturbation Kirchhoff equation −(ε2a+εb∫R3|∇u|2dy)Δu+V(y)u=|u|p−1u,u∈H1(R3),where constants a,b,ε>0 and 1

In this paper, we study the following fractional Kirchhoff equation (a+b∫R3|(−Δ)s2u|2dx)(−Δ)su=λu+μ|u|q−2u+|u|p−2uinR3,with a prescribed mass ∫R3|u|2dx=c2,where s∈(34,1), a, b, c>0, 20 and λ∈R as a Lagrange multiplier. By decomposing Pohozaev set and constructing fiber map, the existence and properties of normalized ground states are established.

In this manuscript, it is considered existence and multiplicity of solutions for a system involving the -Laplacian operator which are related to several applications such as electrorheological fluids, image processing, robotics and space technology. A first solution for the system considered is obtained, under general conditions, by combining sub-supersolutions with a minimization argument in convex

In this paper, some new accelerated iterative schemes are proposed to solve the variational inequality problem with a pseudomonotone and uniformly continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested algorithms are obtained without the prior knowledge of the Lipschitz constant of the operator. Some numerical experiments and applications are performed to illustrate

In this paper, we consider a hyperbolic equation with a logarithmic source term. This work is devoted to prove the global existence and the uniform energy decay rates of a weak solution applying the logarithmic Sobolev inequality and modified multiplier method. This result gives us to classify the energy decay rate dependent on the growth near zero on the damping term.

In this article, we consider the global behavior of components of positive nonconstant radial solutions for the Neumann problem with indefinite weight −Δu=λh(x)f(u),inB,∂νu=0,on∂B,where λ>0 is a parameter, B⊆RN(N≥1) is the unit open ball, f∈C([0,∞),[0,∞)) and h∈C(B¯) satisfying ∫Bh(x)dx<0 is the sign-changing function. We determine the intervals of λ in which the above problem has one, two or three

ABSTRACT In this paper, we introduce a new inertial self-adaptive parallel subgradient extragradient method for finding common solution of variational inequality problems with monotone and Lipschitz continuous operators. The stepsize of the algorithm is updated self-adaptively at each iteration and does not involve a line search technique nor a prior estimate of the Lipschitz constants of the cost

In this paper, we give the definition of local variable Morrey–Lorentz spaces Mp(⋅),q(⋅),λloc(Rn) which are a new class of functions. Also, we prove the boundedness of the Hardy–Littlewood maximal operator M and Calderón–Zygmund operators T on these spaces. Finally, we apply these results to the Bochner–Riesz operator Brδ, identity approximation Aε and the Marcinkiewicz operator μΩ on the spaces Mp(⋅)

This paper delves into the flocking behavior of a class of multi-agent systems with symmetrical and asymmetrical delays under hierarchical leadership. First, we present the two corresponding models. Then, mainly using mathematical induction and considering the nature of differential and quadratic functions, we prove that the group can realize flocking with the two types of delays under certain conditions

Although Strichartz estimates have been widely applied for the nonlinear dispersive equations like Schr o¨dinger equation and wave equation in Besov spaces, it is rare in nonlinear kinetic type equations such as Vlasov-Poisson equation. In this paper, we are concerned about the dispersive estimates for the kinetic transport equation in Besov spaces, which could be applied to establish Strichartz estimates

ABSTRACT We consider an anisotropic (p,2)-equation, with a parametric and superlinear reaction term. We show that for all small values of the parameter the problem has at least five nontrivial smooth solutions, four with constant sign and the fifth nodal (sign-changing). The proofs use tools from critical point theory, truncation and comparison techniques, and critical groups.

In this paper, we establish some new properties of (ω,c)-periodic and asymptotically (ω,c)-periodic functions, then we apply them to study the existence and uniqueness of mild solutions of these types to the following semilinear fractional differential equations: (1) {cDtαu(t)=Au(t)+cDtα−1f(t,u(t)),1<α<2,t∈R,u(0)=0(1) and (2) {cDtαu(t)=Au(t)+cDtα−1f(t,u(t−h)),1<α<2,t,h∈R+,u(0)=0(2) where cDtα(⋅)(1<α<2)

We consider the inverse problem of potential reconstruction from scattering data concerning a 1D model of optical potential introduced by Morillon and Romain [Dispersive and global spherical optical model with a local energy approximation for the scattering of neutrons by nuclei from 1 keV to 300 MeV. Phys Rev C. 2004;70:014601] in the context of nuclear reactions. We show that the inverse method of

In this paper, the exponential synchronization of fractional-order multi-links complex dynamical networks (CDNs) is studied based on non-periodically intermittent control. By means of the Lyapunov method and graph-theoretic approach, a Lyapunov-type theorem is provided based on the existence of vertex-Lyapunov functions. Then by giving the specific vertex-Lyapunov functions, a coefficients-type theorem

In this paper, we establish the existence and uniqueness of pseudo-almost periodic C0-solutions to the evolution equations with nonlocal initial conditions in Banach space. Upon making some appropriate assumptions, the existence and the uniqueness of pseudo-almost periodic C0-solutions to the evolution equations with nonlocal initial conditions are obtained.

This paper focuses on the traveling waves for a nonlocal dispersal SIR model with renewal and spatio-temporal delay. By Schauder's fixed point theorem, the prior estimate, limit theory and analysis techniques, the existence and asymptotic behaviors of traveling waves are obtained, which essentially generalize the results of nonlocal SIR models without renewal and delay. Especially, it is difficult

We consider initial boundary value problems for one-dimensional diffusion equation with time-fractional derivative of order α∈(0,1) which are subject to non-zero Neumann boundary conditions. We prove the uniqueness for an inverse coefficient problem of determining a spatially varying potential and the order of the time-fractional derivative by Dirichlet data at one end point of the spatial interval

In this paper, we mainly investigate some new asymptotic properties on mild solutions to a fractional evolution equation in Banach spaces. Under local, global and mixed Lipschitz type conditions on the second variable for neutral and forced functions respectively, we establish some existence results for pseudo (ω,k)-Bloch periodic and pseudo S-asymptotically (ω,k)-Bloch periodic mild solutions to the

This paper concerns with the Cauchy problem of the 1-D bipolar hydrodynamic model for semiconductors, a system of Euler-Poisson equations with time-dependent damping effects −J(1+t)−λ and −K(1+t)−λ for −1<λ<1. Here, we consider a more physical case that allows the two pressure functions can be different and the doping profile can be non-zero. Different from the previous study [Li HT, Li JY, Mei. M

This paper deals with a mathematical model for tumor growth with angiogenesis and a necrotic core. The problem is a nonlinear problem which has two free boundaries: the external boundary of the tumor and the external boundary of the internal necrotic core. Using the implicit function theorem, the relationship between the two free boundaries is studied. The asymptotic stability of the unique steady-state

In this paper, we qualitatively study the effect of the Coriolis force on traveling waves of the rotation-two-component Camassa–Holm system in the rotating fluid, which is a model in the equatorial water waves, from the perspective of dynamical systems. We obtain the explicit critical rotational speed Ω=12(A+c) (A is a parameter of the system characterizing a linear underlying shear flow and c is the

In this work, we study the existence, uniqueness and regularity of the solution to a semilinear Cauchy–Dirichlet problem with variable coefficients, using the Faedo–Galerkin method. We applied this study to a nonhomogeneous Burgers problem considered in a nonparabolic domain. We give a new regularity result of the solution in an anisotropic Sobolev space.

In this paper, by applying the differential equation techniques and using integral representations, we obtain the Kummer-type transformations of k-hypergeometric functions 1F1,k((a,k);(b,k);x) and 2F2,k((a,k),(d,k);(b,k),(c,k);x), which include known results as special cases.

In this paper, we deal with the fractional p(.,.)-Laplacian problem with nonlocal Neumann boundary conditions {(−Δ)p(.,.)su+|u|p¯(x)−2u=λV1(x)|u|q(x)−2u,inΩ,Ns,p(.,.)u=μV2(x)|u|r(x)−2u,onRN∖Ω,here λ,μ>0 are parameters and V1,V2 are two nonnegative weighted functions. The domain Ω⊂RN (N≥1) is smooth and bounded, p¯(x)=p(x,x),q,r are continuous bounded functions. Applying the Ekeland principle and the

This paper studies the existence of nonnegative solutions for the following parabolic problem {Lωu+∂u∂t=0,inRd×(0,T),u(x,0)=u0(x),inRd,where T>0, Lω is a selfadjoint operator associated with a regular Dirichlet form Q, the initial value u0∈L2(Rd), u0≥0 is a Borel measurable function.

Motivated by computing medians and means, two proximal splitting methods, backward-backward scheme introduced by Passty [Ergodic convergence to a zero of the sum of monotone operators in Hilbert spaces. J Math Anal Appl. 1979;72:383–390.] and barycentric method introduced by Lehdili and Lemaire [Metric spaces of non-positive curvature. Berlin: Springer; 1999.] are investigated in Hadamard space setting

This paper studies the existence, uniqueness, asymptotic and Sp-globally exponential stability of Stepanov-like pseudo almost automorphic solution to Lotka–Volterra recurrent neural networks (LVRNNs) with time-varying delays on time scales by applying D-matrix theory, Banach fixed point theorem, constructing a suitable Lyapunov functional and the theory of time scales calculations. An example and simulations

We consider a one-dimensional thermoelastic Timoshenko system, where the heat conduction is given by Green and Naghdi theories and acting on shear force. We prove that the unique damping given by the memory is sufficiently strong to stabilize the system exponentially, depending on a new relationship between the coefficients of the system and under some assumptions on the kernel of the memory term.

We consider variational inequalities governed by strongly pseudomonotone vector fields on Hadamard manifolds. The existence and uniqueness results of the solution, linear convergence, error estimates and finite convergence for sequences generated by a modified projection method for solving variational inequalities are investigated. Some examples and numerical experiments are also given to illustrate

Based on the well-known Brouwder fixed-point theorem in this paper we will present a variety of collectively coincidence-type results for general classes of maps. Our theory will automatically generate analytic alternatives and minimax inequalities.

This paper deals with the blw-up problem of a system of two coupled nonlinear focusing Schrödinger equations. By using localized virial estimates, we establish a blow-up criteria for non-radial solutions without the hypothesis of finite variance.

In this paper, an equilibrium problem for two elastic bodies connected by a thin junction (bridge) is analyzed. An existence of solutions is proved. Passages to limits are justified with respect to the rigidity parameter of the junction. In particular, the rigidity parameter tends to infinity and to zero. Limit models are investigated.

This paper deals with the numerical treatment of time-dependent singularly perturbed convection–diffusion–reaction equations with delay. In the considered equations, the highest order derivative term is multiplied by a perturbation parameter, ε taking arbitrary value in the interval (0,1]. For small ε, the solution of the equations exhibits a boundary layer on the right side of the spatial domain.

In this paper, an orthogonal basis for the space of linear splines based on linear B-splines is introduced. Some properties and modifications of this basis are investigated, then operational matrices of integration in collocation points are obtained using stable formula. Theoretical considerations are discussed. Applications to the numerical solutions for some linear and nonlinear inverse problems

ABSTRACT In this paper, we study the existence and multiplicity of weak solutions to a (p1(x);p2(x))-Laplacian problem. By means of variational methods, mountain pass lemma and its Z2 symmetric version, we establish the existence and multiplicity of solutions.

ABSTRACT In this paper, we are concerned with an incompressible and inviscid conducting fluid in the presence of surface tension and horizontal electric field. It is obtained the local-in-time estimates on the interface in H(3/2)k+1 and the velocity fields in H(3/2)k by using the method introduced by Shatah and Zeng [A priori estimates for fluid interface problems. Commun Pure Appl Math. 2008;61(6):848–876]

This work deals with a class of nonlinear viscoelastic wave equations with strong damping and variable exponent sources. The main interest of this paper compared to many previous works in the literature is able to use the idea of potential well method to study both the finite time blow-up for solutions starting from the unstable sets and decay estimate for global solutions starting in the potential

In this paper, based on a perturbation argument and fully exploring the nonlinear structure of the considered system, we establish the global existence to the three-dimensional generalized incompressible Hall-MHD equations for a class of large initial data, whose Lp,1≤p≤∞ norms can be arbitrarily large. Our obtained result improves considerably the recent result in Li et al. [A class large solution

Fractional order partial differential equations are very important mathematical models in describing lots of anomalous dynamic behaviors in multiple disciplines. This paper focuses upon the fractional order hyperbolic equation, which is influenced by different types of time-dependent oscillating coefficients on the principal operator part. We apply the essential techniques from harmonic analysis and

In this paper, we consider the Cauchy problem for the nonlinear modified Helmholtz equation (CMH) associated with a fractional Laplacian. The data in the problem including the final data and the source function are studied as random data. The CMH problem is severely ill-posed in Hadamard's sense so that the Fourier truncation method associated with some techniques in nonparametric regression is used

In this paper, we study the existence of solutions for integrodifferential Schrödinger equations of the form −LKu+V(x)u=f(x,u)in R,where −LK is a nonlocal operator with a measurable kernel which satisfies ‘structural properties’, more general than the standard kernel of fractional Laplacian operator, V is a bounded potential, and the nonlinear term f(x,u) has critical exponential growth with respect

In this paper, we are concerned with the Riemann problem for the generalized pressureless Euler equations with a composite source term, which covers the important Eulerian droplet model associated with aircrafts and airways. The Riemann solutions exhibit exactly two types of structures: delta-shocks and vacuum solutions. The generalized Rankine–Hugoniot conditions of the delta shock wave are established

We consider a multilayer hyperbolic-parabolic PDE system which constitutes a coupling of 3D thermal – 2D elastic – 3D elastic dynamics, in which the boundary interface coupling between 3D fluid and 3D structure is realized via a 2D elastic equation. Our main result here is one of strong decay for the given multilayered – heat system. That is, the solution to this composite PDE system is stabilized

Let X be a ball quasi-Banach function space on Rn and HX(Rn) the associated Hardy space. In this article, under the assumptions that the Hardy–Littlewood maximal operator satisfies some Fefferman–Stein vector-valued inequality on X and is bounded on the associated space of X as well as under a lower bound assumption on the X-quasi-norm of the characteristic function of balls, the authors show that

ABSTRACT We consider a recent plate model obtained as a scaled limit of the three-dimensional Biot system of poro-elasticity. The result is a ‘2.5’-dimensional linear system that couples traditional Euler–Bernoulli plate dynamics to a pressure equation in three dimensions, where diffusion acts only transversely. We allow the permeability function to be time dependent, making the problem non-autonomous

In this paper, we consider the following fractional p&q-Laplacian system involving critical sandwich-type nonlinearities: {(−Δ)ps1u+(−Δ)qs2u=λ|u|r−2u+θαα+β|u|α−2u|v|β,inΩ;(−Δ)ps1v+(−Δ)qs2v=μ|v|r−2v+θβα+β|u|α|v|β−2v,inΩ;u=v=0,inRn∖Ω,where Ω⊂Rn is a bounded domain with smooth boundary, 00 are three parameters, α>1, β>1 satisfy α+β=ps1∗, ps1∗=npn−ps1(p

In this paper, we prove a stability estimate of the conductivity parameters identification problem in cardiac electrophysiology. The propagation of the electrical wave in the heart is described by the monodomain model coupled to an elliptic equation describing the diffusion of the electrical wave in the whole body. Our result concerns both heart and torso conductivity parameters. The main difficulty

This paper is concerned with the nonperiodic Hamiltonian system u′=JL(t)u+JHu′(t,u),t∈R.Inspired by Dolbeault, Esteban and Séré [On the eigenvalues of operators with gaps. Application to Dirac operators. J Funct Anal. 2000;174:208–226], we will reduce the associated linear system to a new linear system with finite Morse index. We will develop an index theory and define the relative Morse index by investigating

We consider the operator Δ(α,β)−I, where Δ(α,β) is the three term recurrence relation for the Jacobi polynomial Rn(α,β)(x) normalized at the point x = 1 and I is the identity operator acting on N. Knowing that for α≥β≥−12, these polynomials satisfy a product formula which provides a hypergroup structure on N, we use the tools of harmonic analysis on this hypergroup to solve the space-time fractional

ABSTRACT In this paper, we investigate the traveling wave solutions of diffusive disease models with a general incidence rate, nonlocal interaction and transmission delay. We prove that a positive traveling wave solution exists if the wave speed is bigger than a threshold value and does not exist if the wave speed is smaller than this value. We also investigate the dependence of this critical wave

ABSTRACT This paper presents the three-dimensional analysis of the stress distribution arising in an isotropic infinite slab with a triaxial ellipsoidal cavity, the surface of which is subjected to the three principal stresses σ1,σ2, and σ3. To satisfy both boundary conditions on the surface of slab and the cavity, harmonic functions in rectangular coordinates are used and double Fourier transform