Infinitely many positive solutions for a nonlocal problem with competing potentials

被引：2

作者：

Yang, Jing ^{[1
]}

机构：

[1] Jiangsu Univ Sci & Technol, Sch Sci, Zhenjiang, Jiangsu, Peoples R China

来源：

BOUNDARY VALUE PROBLEMS | 2020年 / 2020卷 / 01期

关键词：

Competing potentials; Infinitely many solutions; Lyapunov-Schmidt reduction; SCHRODINGER-EQUATION; OBSTACLE PROBLEM; GROUND-STATES; EXISTENCE; REGULARITY; WAVES; DECAY;

D O I：

10.1186/s13661-020-01406-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The present paper deals with a class of nonlocal problems. Under some suitable assumptions on the decay rate of the coefficients, we derive the existence of infinitely many positive solutions to the problem by applying reduction method. Comparing to the previous work, we encounter some new challenges because of competing potentials. By doing some delicate estimates for the competing potentials, we overcome the difficulties and find infinitely many positive solutions.

引用

页数：17

共 24 条

[1] Infinitely many positive solutions for nonlinear equations with non-symmetric potentials [J].

Ao, Weiwei ;

Wei, Juncheng .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2014, 51 (3-4) :761-798

[2] On the existence of a positive solution of semilinear elliptic equations in unbounded domains [J].

Bahri, A ;

Lions, PL .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1997, 14 (03) :365-413

[3]

Bahri A., 1990, Rev. Mat. Iberoam, V6, P1, DOI DOI 10.4171/RMI/92

[4] Decay and analyticity of solitary waves [J].

Bona, JL ;

Li, YA .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 1997, 76 (05) :377-430

[5] Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian [J].

Caffarelli, Luis A. ;

Salsa, Sandro ;

Silvestre, Luis .

INVENTIONES MATHEMATICAE, 2008, 171 (02) :425-461

[6]

Cerami G., 2006, MILAN J MATH, V1, P47, DOI DOI 10.1007/S00032-006-0059-Z

[7] On Some Scalar Field Equations with Competing Coefficients [J].

Cerami, Giovanna ;

Pomponio, Alessio .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2018, 2018 (08) :2481-2507

[8] Infinitely Many Positive Solutions to Some Scalar Field Equations with Nonsymmetric Coefficients [J].

Cerami, Giovanna ;

Passaseo, Donato ;

Solimini, Sergio .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2013, 66 (03) :372-413

[9] CONCENTRATION PHENOMENA FOR THE NONLOCAL SCHRODINGER EQUATION WITH DIRICHLET DATUM [J].

Davila, Juan ;

del Pino, Manuel ;

Dipierro, Serena ;

Valdinoci, Enrico .

ANALYSIS & PDE, 2015, 8 (05) :1165-1235

[10] Concentrating standing waves for the fractional nonlinear Schrodinger equation [J].

Davila, Juan ;

del Pino, Manuel ;

Wei, Juncheng .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 256 (02) :858-892

← 1 2 3 →