A solution to a slightly subcritical elliptic problem with non-power nonlinearity

被引：14

作者：

Clapp, Monica ^{[1
]}

Pardo, Rosa ^{[2
]}

Pistoia, Angela ^{[3
]}

Saldana, Alberto ^{[1
]}

机构：

[1] Univ Nacl Autonoma Mexico, Inst Matemat, Ciudad Univ, Ciudad De Mexico 04510, Mexico

[2] Univ Complutense Madrid, Fac Ciencias Quim, Dept Anal Matemat & Matemat Aplicada, Madrid 28040, Spain

[3] Sapienza Univ Roma, Dipartimento Metodi & Modelli Matemat, Via Antonio Scarpa 16, I-00161 Rome, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2021年 / 275卷

关键词：

Blow-up solutions; Critical Sobolev exponent; Ljapunov-Schmidt reduction; CRITICAL-POINTS; POSITIVE SOLUTIONS; CRITICAL EXPONENT; ROBIN FUNCTION; EXISTENCE;

D O I：

10.1016/j.jde.2020.11.030

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a slightly subcritical Dirichlet problem with a non-power nonlinearity in a bounded smooth domain. For this problem, standard compact embeddings cannot be used to guarantee the existence of solutions as in the case of power-type nonlinearities. Instead, we use a Ljapunov-Schmidt reduction method to show that there is a positive solution which concentrates at a non-degenerate critical point of the Robin function. This is the first existence result for this type of generalized slightly subcritical problems. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：418 / 446

页数：29

共 20 条

[1] ON A VARIATIONAL PROBLEM WITH LACK OF COMPACTNESS - THE TOPOLOGICAL EFFECT OF THE CRITICAL-POINTS AT INFINITY
BAHRI, A
LI, YY
REY, O
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 1995, 3 (01): : 67 - 93
[2] ON A NONLINEAR ELLIPTIC EQUATION INVOLVING THE CRITICAL SOBOLEV EXPONENT - THE EFFECT OF THE TOPOLOGY OF THE DOMAIN
BAHRI, A
CORON, JM
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1988, 41 (03) : 253 - 294
[3] On the existence and the profile of nodal solutions of elliptic equations involving critical growth
Bartsch, T
Micheletti, AM
Pistoia, A
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2006, 26 (03) : 265 - 282
[4] A PRIORI ESTIMATES FOR POSITIVE SOLUTIONS TO SUBCRITICAL ELLIPTIC PROBLEMS IN A CLASS OF NON-CONVEX REGIONS
Castro, Alfonso
Pardo, Rosa
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2017, 22 (03): : 783 - 790
[5] A priori bounds for positive solutions of subcritical elliptic equations
Castro, Alfonso
Pardo, Rosa
[J]. REVISTA MATEMATICA COMPLUTENSE, 2015, 28 (03): : 715 - 731
[6] A priori estimates for some elliptic equations involving the p-Laplacian
Damascelli, Lucio
Pardo, Rosa
[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2018, 41 : 475 - 496
[7] DEFIGUEIREDO DG, 1982, J MATH PURE APPL, V61, P41
[8] Gidas B., 1981, Commun. Partial Differ. Equ., V8, P883, DOI 10.1080/03605308108820196
[9] On the nondegeneracy of the critical points of the Robin function in symmetric domains
Grossi, M
[J]. COMPTES RENDUS MATHEMATIQUE, 2002, 335 (02) : 157 - 160
[10] HAN ZC, 1991, ANN I H POINCARE-AN, V8, P159

← 1 2 →