On a Critical Exponential p & N Equation Type: Existence and Concentration of Changing Solutions

被引：7

作者：

Costa, Gustavo S. ^{[1
]}

Figueiredo, Giovany M. ^{[1
]}

机构：

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

来源：

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY | 2022年 / 53卷 / 01期

关键词：

p& N Laplacian operator; Del Pino; Felmer's Penalization method; POSITIVE SOLUTIONS; ELLIPTIC EQUATION; NODAL SOLUTIONS; CRITICAL GROWTH; POTENTIALS; NONLINEARITY; MULTIPLICITY;

D O I：

10.1007/s00574-021-00257-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study a class of quasilinear equation with exponential critical growth. More precisely, we show existence of a family of nodal solutions, i.e, sign-changing solutions for the problem {-div (a (epsilon(p)|del u|(p)) epsilon(p)|del u|(p-2) del u) + V( z)b (|u|(p) |u|(p-2)u = f (u) in R-N, u is an element of W-1,W- p(R-N) boolean AND W-1,W-N (R-N). Such nodal solutions concentrate on the minimum points set of the potential V, changes sign exactly once in R-N and have exponential decay at infinity. Herewe use variational methods and Del Pino and Felmer's technique (Del Pino and Felmer 1996) in order to overcome the lack of compactness.

引用

页码：243 / 280

页数：38

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