R3中一类带有凹凸非线性项的Schr?dinger-Kirchhoff方程的无穷多解
Infinitely Many Solutions for Schr?dinger-Kirchhoff Equation with Concave-convex Nonlinearities in R3
赵莉 1叶一蔚1
作者信息
- 1. 重庆师范大学数学科学学院,重庆沙坪坝 401331
- 折叠
摘要
研究一类带有凹凸非线性项的Schrödinger-Kirchhoff方程,其中位势函数不必满足强制性条件,凹项满足次线性增长性条件,并且凸项在无穷远处满足超三次线性增长性条件和在原点处满足超线性增长性条件.利用Bartsch的喷泉定理证明了对任意的μ∈R,凹凸非线性项的Schrödinger-Kirchhoff方程都存在无穷多个高能量解,丰富和推广了已有的结论.
Abstract
A class of Schrödinger-Kirchhoff type equations with concave-convex nonlinearity in abstract form is studied,where the potential is not coercive,the concave term is of sublinear growth,the convex term satisfies the 3-superlinear growth condition at infinity and the superlinear growth condition at the origin.By Fountain theorem,we prove that,for all μ∈R,the Schrödinger-Kirchhoff type equations with concave-convex nonlinearity possesses infinitely many high-energy solutions,which improves and generalizes some known results in the literature.
关键词
Schrödinger-Kirchhoff方程/凹凸非线性项/喷泉定理/无穷多解Key words
Schrödinger-Kirchhoff equation/concave-convex nonlinearities/Fountain Theorem/infinitely many solutions引用本文复制引用
出版年
2024
NETL
NSTL
万方数据