EXISTENCE OF SOLUTIONS FOR A NONHOMOGENEOUS KIRCHHOFF-SCHRODINGER TYPE EQUATION IN R2 INVOLVING UNBOUNDED OR DECAYING POTENTIALS

被引：7

作者：

Albuquerque, Francisco S. B. ^{[1
]}

Bahrouni, Anouar ^{[2
]}

Severo, Uberlandio B. ^{[3
]}

机构：

[1] Univ Estadual Paraiba, Dept Matemat, BR-58429500 Campina Grande, Paraiba, Brazil

[2] Univ Monastir, Math Dept, Fac Sci, Monastir 5019, Tunisia

[3] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba, Brazil

来源：

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2020年 / 56卷 / 01期

关键词：

Kirchhoff-Schrodinger equation; Trudinger-Moser inequality; Ex-ponential growth; NONTRIVIAL SOLUTIONS; POSITIVE SOLUTIONS; CRITICAL GROWTH; ELLIPTIC-EQUATIONS; MULTIPLICITY;

D O I：

10.12775/TMNA.2020.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the following nonhomogeneous Kirchhoff-Schrodinger equation: m(integral(R2) vertical bar del u vertical bar(2) dx + integral(R2) V (vertical bar x vertical bar)u(2) dx) [-Delta u + V(vertical bar x vertical bar)u] = Q(vertical bar x vertical bar)f(u) + epsilon h(x), for x is an element of R-2, where m, V, Q and f are continuous functions, epsilon is a small parameter and h not equal 0. When f has exponential growth by means of a Trudinger-Moser type inequality, the Mountain Pass Theorem and Ekeland's Variational Principle in weighted Sobolev spaces are applied in order to establish the existence of at least two weak solutions for this equation.

引用

页码：263 / 281

页数：19

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