Ground state solutions for a fractional Schrodinger equation with critical growth

被引：22

作者：

Ambrosio, Vincenzo ^{[1
]}

Figueiredo, Giovany M. ^{[2
]}

机构：

[1] Univ Urbino Carlo Bo, Dipartimento Sci Pure & Applicate DiSPeA, Piazza Repubbl 13, I-61029 Urbino, Pesaro Urbino, Italy

[2] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil

来源：

ASYMPTOTIC ANALYSIS | 2017年 / 105卷 / 3-4期

关键词：

Fractional Laplacian; monotonicity trick; critical exponent; compactness lemma; SCALAR FIELD-EQUATIONS; EXISTENCE; LAPLACIAN; SYMMETRY;

D O I：

10.3233/ASY-171438

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we investigate the existence of nontrivial ground state solutions for the following fractional scalar field equation (-Delta)(s)u + V(x)u = f(u) in R-N, where s is an element of (0, 1), N > 2s, (-Delta) s is the fractional Laplacian, V : R-N -> R is a bounded potential satisfying suitable assumptions, and f is an element of C-1,C-beta (R, R) has critical growth. We first analyze the case V constant, and then we develop a Jeanjean-Tanaka argument [Indiana Univ. Math. J. 54 ( 2005), 443-464] to deal with the non autonomous case. As far as we know, all results presented here are new.

引用

页码：159 / 191

页数：33

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