当前位置: X-MOL 学术Commun. Contemp. Math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Generalized linking theorem with applications to nonautonomous Hamiltonian systems and Dirac equations on compact spin manifold
Communications in Contemporary Mathematics ( IF 1.6 ) Pub Date : 2020-03-09 , DOI: 10.1142/s0219199720500169
Yanyan Liu 1, 2 , Chong Li 1, 3 , Shujie Li 1
Affiliation  

Let (M,g) be a Riemannian manifold with finite volume and U be a linear topological space. We consider the strongly indefinite superlinear problem Au = |u|p2u + uψ(x,u),u H, where A : L2(M,U) L2(M,U) is a self-adjoint linear operator, H is a real Hilbert space with the compact embedding HLp(M,U) if p [2,q) for some q > 2, and ( uψ(x,u),u) C(|u|2 + |u|p). We obtain the existence of two solutions provided that p < 2 + p0 and C < C0 for a certain choice of p0, C0 > 0. Moreover, we prove that, if p 2 and C small enough, there exist prescribed number of nontrivial solutions. As applications, the corresponding results hold true for nonautonomous Hamiltonian systems and Dirac equations on compact spin manifold.

中文翻译:

广义链接定理与非自治哈密顿系统和紧自旋流形上的狄拉克方程的应用

(,G)是一个具有有限体积的黎曼流形,并且ü是一个线性拓扑空间。我们考虑强不定超线性问题 一种 = ||p-2 + ψ(X,), H, 在哪里一种 大号2(,ü) 大号2(,ü)是自伴线性算子,H是具有紧嵌入的实希尔伯特空间H大号p(,ü)如果p [2,q)对于一些q > 2, 和( ψ(X,),) C(||2 + ||p). 我们得到两个解的存在,前提是p < 2 + p0C < C0对于某个选择p0,C0 > 0. 此外,我们证明,如果p - 2C足够小,存在规定数量的非平凡解。作为应用,相应的结果适用于非自治哈密顿系统和紧自旋流形上的狄拉克方程。
更新日期:2020-03-09
down
wechat
bug