MULTIPLICITY AND CONCENTRATION OF SOLUTIONS FOR NONLINEAR FRACTIONAL ELLIPTIC EQUATIONS WITH STEEP POTENTIAL

被引：9

作者：

Peng, Song ^{[1
]}

Xia, Aliang ^{[1
]}

机构：

[1] Jiangxi Normal Univ, Dept Math, Nanchang 330022, Jiangxi, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2018年 / 17卷 / 03期

关键词：

Fractional Laplacian; steep potential; Nehari manifold; concave-convex term; POSITIVE SOLUTIONS; SCHRODINGER-EQUATIONS; NEHARI MANIFOLD; STATES;

D O I：

10.3934/cpaa.2018058

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we prove the existence, multiplicity and concentration of non-trivial solutions for the following indefinite fractional elliptic equation with concave-convex nonlinearities: {(-Delta)(alpha)u + V-lambda(x)u = a(x)vertical bar u vertical bar(q-2)u + b(x)vertical bar u vertical bar(p-2)u in R-N, u >= 0 in R-N, where 0 < alpha < 1, N > 2 alpha, 1 < q < 2 < p < 2(alpha)*; with 2(alpha)*= 2N/(N - 2 alpha), the potential V-lambda(x) = lambda V+(x)- V-(x) with V-+/- = max{+/- V, 0} and the parameter lambda > 0. Our multiplicity results are based on studying the decomposition of the Nehari manifold.

引用

页码：1201 / 1217

页数：17

共 50 条

[31] Multiplicity results for elliptic fractional equations with subcritical term [J].

Bisci, Giovanni Molica ;

Radulescu, Vicentiu D. .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2015, 22 (04) :721-739

[32] Multiplicity of positive solutions for fractional elliptic systems involving sign-changing weight [J].

Fan, Haining .

BOUNDARY VALUE PROBLEMS, 2017,

[33] Multiplicity results for elliptic fractional equations with subcritical term [J].

Giovanni Molica Bisci ;

Vicenţiu D. Rădulescu .

Nonlinear Differential Equations and Applications NoDEA, 2015, 22 :721-739

[34] Multiple positive solutions for nonlinear critical fractional elliptic equations involving sign-changing weight functions [J].

Quaas, Alexander ;

Xia, Aliang .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2016, 67 (03)

[35] Multiple positive solutions for nonlinear critical fractional elliptic equations involving sign-changing weight functions [J].

Alexander Quaas ;

Aliang Xia .

Zeitschrift für angewandte Mathematik und Physik, 2016, 67

[36] Multiplicity and Concentration Properties for Fractional Choquard Equations with Exponential Growth [J].

Liang, Shuaishuai ;

Shi, Shaoyun ;

Nguyen, Thin Van .

JOURNAL OF GEOMETRIC ANALYSIS, 2024, 34 (12)

[37] Existence and multiplicity of positive solutions for a class of nonlinear elliptic problems [J].

Aghajani, Asadollah ;

Shamshiri, Jamile ;

Yaghoobi, Farajollah Mohammadi .

TURKISH JOURNAL OF MATHEMATICS, 2013, 37 (02) :286-298

[38] Multiplicity and concentration of solutions to a fractional p-Laplace problem with exponential growth [J].

Thin, Nguyen Van .

ANNALES FENNICI MATHEMATICI, 2022, 47 (02) :603-639

[39] Multiplicity of positive solutions for a class of fractional Schrodinger equations via penalization method [J].

Ambrosio, Vincenzo .

ANNALI DI MATEMATICA PURA ED APPLICATA, 2017, 196 (06) :2043-2062

[40] Existence and multiplicity of solutions for a class of fractional elliptic systems [J].

Manassés de Souza .

Collectanea Mathematica, 2020, 71 :103-122

← 1 2 3 4 5 →