Existence of Solutions for a Quasilinear Schr?dinger Equation with Potential Vanishing  

作　　者：Yan-fang XUE Jian-xin HAN Xin-cai ZHU 

机构地区：[1]School of Mathematics and Statistics,Xinyang Normal University,Henan 464000,China

出　　处：《Acta Mathematicae Applicatae Sinica》2023年第3期696-706,共11页应用数学学报（英文版）

基　　金：the National Natural Science Foundation of China(No.11901499 and No.11901500);Nanhu Scholar Program for Young Scholars of XYNU(No.201912)。

摘　　要：We study the following quasilinear Schrodinger equation-△u+V(x)u-△(u^(2))u=K(x)g(u),x∈R^(3),where the nonlinearity g(u)is asymptotically cubic at infinity,the potential V(x)may vanish at infinity.Under appropriate assumptions on K(x),we establish the existence of a nontrivial solution by using the mountain pass theorem.

关 键 词：quasilinear SchrOdinger equation vanishing potential asymptotically cubic mountain pass theorem 

分 类 号：O175.29[理学—数学]