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Infinitely many sign-changing solutions for modified Kirchhoff-type equations in ℝ3
Complex Variables and Elliptic Equations ( IF 0.6 ) Pub Date : 2020-08-24 , DOI: 10.1080/17476933.2020.1807964
Chen Huang 1 , Gao Jia 2
Affiliation  

ABSTRACT

Consider a class of modified Kirchhoff-type equations (1+bR3|u|2dx)Δu+V(x)u12uΔ(u2)=f(u),in R3, where the nonlinear term f is 4-superlinear at infinity. By using the method of invariant sets of descending flow, the existence of a sign-changing solution is obtained. When f is assumed to be odd, we prove that the above problem admits infinitely many sign-changing solutions. Moreover, when V(x)1 and the nonlinearity of power growth f(u)=|u|p2u with 1<p, we establish some existence and non-existence results. For p(1,2][12,), the non-existence result relies on the deduction of some suitable Pohozaev identity. For p(3,4], using the Nehari–Pohozaev manifold, we prove that the above problem admits a ground state solution.



中文翻译:

ℝ3 中修正基尔霍夫型方程的无穷多变号解

摘要

考虑一类修正的基尔霍夫型方程 -(1+电阻3||2dX)Δ+(X)-12Δ(2)=F(), 电阻3,其中非线性项f在无穷远处是 4-超线性的。利用下降流不变集的方法,得到了变号解的存在性。当f被假定为奇数时,我们证明上述问题允许无限多个变号解。此外,当(X)1 和功率增长的非线性 F()=||p-2当 1< p 时,我们建立了一些存在和不存在的结果。为了p(1,2][12,),不存在的结果依赖于一些合适的 Pohozaev 恒等式的推导。为了p(3,4],使用 Nehari-Pohozaev 流形,我们证明上述问题允许基态解。

更新日期:2020-08-24
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