QUASILINEAR SCHRODINGER EQUATIONS WITH SINGULAR AND VANISHING POTENTIALS INVOLVING NONLINEARITIES WITH CRITICAL EXPONENTIAL GROWTH

被引：5
|
作者：
Araujo, Yane Lisley [1 ]
Carvalho, Gilson [1 ]
Clemente, Rodrigo [1 ]
机构：
[1] Univ Fed Rural Pernambuco, Dept Math, BR-52171900 Recife, PE, Brazil
来源：
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2021年 / 57卷 / 01期
关键词：
Variational methods; critical exponential growth; Schodinger equation; unbounded or decaying potentials; ELLIPTIC-EQUATIONS; EXISTENCE; COMPACTNESS; SPACES;
D O I：
10.12775/TMNA.2020.024
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the following class of Schrodinger equations: -Delta(N)u+ V(vertical bar x vertical bar))vertical bar u vertical bar(N-2)u = Q(vertical bar x vertical bar h(u) in R-N, where N >= 2, V, Q: R-N -> R are potentials that can be unbounded, decaying or vanishing at infinity and the nonlinearity h: R -> R has a critical exponential growth concerning the Trudinger Moser inequality. By using a variational approach, a version of the Trudinger Moser inequality and a symmetric criticality type result, we obtain the existence of nonnegative weak and ground state solutions for this class of problems and under suitable assumptions, we obtain a nonexistence result.
引用
收藏
页码：317 / 342
页数：26
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