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
收藏
页码：1993 / 2007
页数：15
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