Critical boundary value problems in the upper half-space

被引：3

作者：

Furtado, Marcelo F. ^{[1
]}

da Silva, Joao Pablo P. ^{[2
]}

机构：

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

[2] Univ Fed Para, Dept Matemat, BR-66075110 Belem, Para, Brazil

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2021年 / 212卷

关键词：

Weighted trace embedding; Critical problems; Nonlinear boundary conditions; Self-similar solutions; Half-space; SELF-SIMILAR SOLUTIONS; POSITIVE SOLUTIONS; CONFORMAL DEFORMATION; SOBOLEV INEQUALITIES; UNIQUENESS THEOREMS; EXISTENCE; MULTIPLICITY; EQUATIONS; CONSTANT;

D O I：

10.1016/j.na.2021.112441

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the critical problem -Delta u - 1/2 (x.del u) = 0 in R-+(N), partial derivative u/partial derivative nu = lambda vertical bar u vertical bar(p-2)u + vertical bar u vertical bar(2)*(-2)u on partial derivative R-+(N), where R-+(N) - {x', x(N)) : x' is an element of RN-1, x(N) > 0} is the upper half-space, N >= 4, nu is the outward normal vector at the boundary and 2 <= p < 2(*) := 2(N - 1)/(N - 2). Using a variational approach, we obtain nonnegative nonzero solutions according to the value of the parameter lambda > 0. (C) 2021 Elsevier Ltd. All rights reserved.

引用

页数：11