Concentration Phenomena for Fractional Elliptic Equations Involving Exponential Critical Growth

被引：22

作者：

Alves, Claudianor O. ^{[1
]}

do O, Joao Marcos ^{[2
]}

Miyagaki, Olimpio H. ^{[3
]}

机构：

[1] Univ Fed Campina Grande, Unidade Acad Matemat, BR-58429900 Campina Grande, PB, Brazil

[2] Univ Fed Paraiba, Dept Math, BR-58051900 Joao Pessoa, PB, Brazil

[3] Univ Fed Juiz de Fora, Dept Math, BR-36036330 Juiz De Fora, MG, Brazil

来源：

ADVANCED NONLINEAR STUDIES | 2016年 / 16卷 / 04期

关键词：

Trudinger-Moser Inequality; Nonlinear Schrodinger Equations; Variational Methods; Mountain Pass Theorem; Lack of Compactness; Critical Growth; Fractional Laplacian; NONLINEAR SCHRODINGER-EQUATION; POSITIVE SOLUTIONS; GROUND-STATES; PERTURBATIONS;

D O I：

10.1515/ans-2016-0097

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we deal with the singular perturbed fractional elliptic problem is an element of(-Delta)(1/2)u + V(z)u = f(u) in IR, where (-Delta)(1/)2u is the square root of the Laplacian and f(s) has exponential critical growth. Under suitable conditions on f(s), we construct a localized bound state solution concentrating at an isolated component of the positive local minimum points of the potential of V as epsilon goes to 0.

引用

页码：843 / 861

页数：19

共 31 条

[1] Alves C. O., 2016, PARTIAL DIFFERENTIAL, V55
[2] Alves CO, 2016, MILAN J MATH, V84, P1, DOI 10.1007/s00032-015-0247-9
[3] Alves CO, 2005, ADV NONLINEAR STUD, V5, P551
[4] On nonlinear perturbations of a periodic elliptic problem in R2 involving critical growth
Alves, CO
do O, JM
Miyagaki, OH
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 56 (05) : 781 - 791
[5] Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7
[6] [Anonymous], 2016, Mathematical Problems in Engineering, DOI [10.1208/s12249-016-0486-2, DOI 10.1155/2016/6408741, DOI 10.1155/2016/9084370]
[7] On some critical problems for the fractional Laplacian operator
Barrios, B.
Colorado, E.
de Pablo, A.
Sanchez, U.
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (11) : 6133 - 6162
[8] Blumenthal RM., 1960, T AM MATH SOC, V95, P263, DOI [DOI 10.1090/S0002-9947-1960-0119247-6, 10.1090/S0002-9947-1960-0119247-6]
[9] A concave-convex elliptic problem involving the fractional Laplacian
Braendle, C.
Colorado, E.
de Pablo, A.
Sanchez, U.
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2013, 143 (01) : 39 - 71
[10] Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates
Cabre, Xavier
Sire, Yannick
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2014, 31 (01): : 23 - 53

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