Quasilinear asymptotically periodic Schrodinger equations with critical growth

被引：200

作者：

Silva, Elves A. B. ^{[1
]}

Vieira, Gilberto F. ^{[2
]}

机构：

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

[2] Univ Fed Campina Grande, Unidade Acad Ciencias Exatas & Nat, Ctr Formacao Prof, BR-58900000 Cajazeiras, PB, Brazil

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2010年 / 39卷 / 1-2期

关键词：

SCALAR FIELD-EQUATIONS; SOLITON-SOLUTIONS; ELLIPTIC-EQUATIONS; EXISTENCE; R-2;

D O I：

10.1007/s00526-009-0299-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is established the existence of solutions for a class of asymptotically periodic quasilinear elliptic equations in RN with critical growth. Applying a change of variable, the quasilinear equations are reduced to semilinear equations, whose respective associated functionals are well defined in H(1)(R(N)) and satisfy the geometric hypotheses of the Mountain Pass Theorem. The Concentration-Compactness Principle and a comparison argument allow to verify that the problem possesses a nontrivial solution.

引用

页码：1 / 33

页数：33

共 25 条

[1] On nonlinear perturbations of a periodic elliptic problem in R2 involving critical growth [J].

Alves, CO ;

do O, JM ;

Miyagaki, OH .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 56 (05) :781-791

[2]

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

[3]

[Anonymous], 1983, ELLIPTIC PARTIAL DIF

[4]

[Anonymous], 1996, VARIATIONAL METHODS, DOI DOI 10.1007/978-3-662-03212-1

[5]

BERESTYCKI H, 1983, ARCH RATION MECH AN, V82, P313

[6]

BERESTYCKI H, 1983, CR ACAD SCI I-MATH, V297, P307

[7]

BERESTYCKI H, 1995, NODEA-NONLINEAR DIFF, V2, P533

[8] POSITIVE SOLUTIONS OF NON-LINEAR ELLIPTIC-EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS [J].

BREZIS, H ;

NIRENBERG, L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1983, 36 (04) :437-477

[9] Solutions for a quasilinear Schrodinger equation: a dual approach [J].

Colin, M ;

Jeanjean, L .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 56 (02) :213-226

[10] Solitary waves for a class of quasilinear Schrodinger equations in dimension two [J].

do O, Joao Marcos ;

Severo, Uberlandio .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2010, 38 (3-4) :275-315

← 1 2 3 →