GROUND STATES OF SOME FRACTIONAL SCHRODINGER EQUATIONS ON RN

被引：15

作者：

Chang, Xiaojun ^{[1
,2
]}

机构：

[1] NE Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China

[2] Jilin Univ, Coll Math, Changchun 130012, Jilin, Peoples R China

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2015年 / 58卷 / 02期

关键词：

ground states; fractional Schrodinger equation; variational methods; POSITIVE SOLUTIONS; EXISTENCE; REGULARITY; LAPLACIAN; SYMMETRY;

D O I：

10.1017/S0013091514000200

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study a time-independent fractional Schrodinger equation of the form (-Delta)(s)u + V (x)u = g(u) in R-N, where N >= 2, s is an element of (0, 1) and (-Delta)(s) is the fractional Laplacian. By variational methods, we prove the existence of ground state solutions when V is unbounded and the nonlinearity g is subcritical and satisfies the following geometry condition: lim sup(t -> 0+) 2 integral(t)(0) g(tau) d tau/t(2) < inf sigma ((-Delta)(s) + V(x)) < lim inf (t ->+infinity) 2 integral(t)(0) g(tau) d tau/t(2)

引用

页码：305 / 321

页数：17

共 37 条

[1]

Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7

[2] Multiplicity results for some nonlinear Schrodinger equations with potentials [J].

Ambrosetti, A ;

Malchiodi, A ;

Secchi, S .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2001, 159 (03) :253-271

[3]

[Anonymous], 1986, REGIONAL C SERIES MA

[4] On the Schrodinger Equation in RN under the Effect of a General Nonlinear Term [J].

Azzollini, A. ;

Pomponio, A. .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2009, 58 (03) :1361-1378

[5] On some critical problems for the fractional Laplacian operator [J].

Barrios, B. ;

Colorado, E. ;

de Pablo, A. ;

Sanchez, U. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (11) :6133-6162

[6] EXISTENCE AND MULTIPLICITY RESULTS FOR SOME SUPERLINEAR ELLIPTIC PROBLEMS ON R(N) [J].

BARTSCH, T ;

WANG, ZQ .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1995, 20 (9-10) :1725-1741

[7]

Bartsch T, 2005, HBK DIFF EQUAT STATI, V2, P1, DOI 10.1016/S1874-5733(05)80009-9

[8] A concave-convex elliptic problem involving the fractional Laplacian [J].

Braendle, C. ;

Colorado, E. ;

de Pablo, A. ;

Sanchez, U. .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2013, 143 (01) :39-71

[9]

Brezis H., 2011, Functional analysis, DOI DOI 10.1007/978-0-387-70914-7

[10] Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates [J].

Cabre, Xavier ;

Sire, Yannick .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2014, 31 (01) :23-53

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