SCHRODINGER-KIRCHHOFF-HARDY p-RACTIONAL EQUATIONS WITHOUT THE AMBROSETTI-RABINOWITZ CONDITION

被引：10

作者：

Fiscella, Alessio ^{[1
]}

机构：

[1] Univ Estadual Campinas, Dept Matemat, IMECC, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP, Brazil

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2020年 / 13卷 / 07期

基金：

巴西圣保罗研究基金会;

关键词：

Schrodinger-Kirchhoff equations; existence of entire solutions; fractional p-Laplacian operator; Hardy coefficients; variational methods; NONTRIVIAL SOLUTIONS; EXISTENCE THEOREMS; MULTIPLICITY; LAPLACIAN; SYSTEMS;

D O I：

10.3934/dcdss.2020154

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to the study of the following Schrodinger-Kirchhoff-Hardy equation in R-n M(integral integral(R2n) vertical bar u(x) - u(y)vertical bar(p)/vertical bar x - y vertical bar(n) vertical bar ps dxdy) (-Delta)(p)(s)u + V(x)vertical bar u vertical bar(p-2) u-u vertical bar u vertical bar(p-2)u/vertical bar x vertical bar p(s) = f(x, u), where (-Delta)(p)(s) is the fractional p-Laplacian, with s is an element of (0, 1) and p > 1, dimension n > ps, M models a Kirchhoff coefficient, V is a positive potential, f is a continuous nonlinearity and mu is a real parameter. The main feature of the paper is the combination of a Kirchhoff coefficient and a Hardy term with a suitable function f which does not necessarily satisfy the Ambrosetti-Rabinowitz condition. Under different assumptions for f and restrictions for mu, we provide existence and multiplicity results by variational methods.

引用

页码：1993 / 2007

页数：15

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