R^(3)中一类带有凹凸非线性项的Schrödinger-Kirchhoff方程的无穷多解  

Infinitely Many Solutions for Schrödinger-Kirchhoff Equation with Concave-convex Nonlinearities in R^(3)

作　　者：赵莉 叶一蔚 ZHAO Li;YE Yi-wei(College of Mathematical Science,Chongqing Normal University,Shapingba401331,Chongqing)

机构地区：[1]重庆师范大学数学科学学院,重庆沙坪坝401331

出　　处：《商洛学院学报》2024年第4期18-24,共7页Journal of Shangluo University

基　　金：国家自然科学基金项目(12171062)。

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。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 allμ∈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 

分 类 号：O176.3[理学—数学]