R³ 上带有凹凸非线性项的Schrodinger-Poisson系统的无穷多解

打开文本图片集

中图分类号：0176.3 文献标识码：A 文章编号：1674-0033（2025）04-0019-08

Abstract：A class of Schrodinger-Poisson systems with concave-convex nonlinear terms is studied，in which the potential function v（x）∈C（R3，R） doesnot have to satisfy the mandatory condition.Under more general concave convex nonlinear conditions，by introducing the variational framework and combining the detailedestimationofnon-local terms，the fountain theoreminthecritical point theory isutilized to prove that forany μ∈R system，there exist infinitely many high Π-Π energy solutions.This breaks through the mandatory restrictions on the potential function in traditional studies and establishes the existence theory of multiple property solutions applicable to a wider range of concave-convex nonlinear conditions. It further expands the understanding of the solutions of such complex systems.

Keywords：Schrodinger-Poisson system; Fountain Theorem; high energy solution

薛定谔-泊松系统由薛定谔方程和泊松方程耦合而成，用于描述量子力学中粒子在势场中的复杂行为。（剩余10752字）