On a nonlinear problem with zero Dirichlet boundary condition

被引：4

作者：

Sharaf, Khadijah ^{[1
]}

机构：

[1] King Abdulaziz Univ, Dept Math, Jeddah, Saudi Arabia

来源：

APPLICABLE ANALYSIS | 2017年 / 96卷 / 09期

关键词：

Nonlinear elliptic P; D; E; lack of compactness; critical points at infinity; 35J20; 35J60; SCALAR-CURVATURE PROBLEM; S-N; EXISTENCE; COMPACTNESS; DIMENSION; MANIFOLDS; SPHERE;

D O I：

10.1080/00036811.2016.1220548

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are concerned with the following PDE: -u = K(x)u(n+2/n-2), u > 0 in Omega, u = 0, on partial derivative Omega, where Omega is a bounded domain of R-n, n >= 3, and K : (Omega) over bar -> R is a given function. We provide a complete description of the loss of compactness of the equation under the assumption that K is strictly decreasing in the outward normal direction on partial derivative Omega and flat near its critical points. As product, we prove an existence result through an Euler-Poincare characteristic argument.

引用

页码：1466 / 1482

页数：17

共 50 条

[1] A free boundary problem with nonlinear advection and Dirichlet boundary condition
Ding, Ning
Cai, Jingjing
Xu, Li
[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2023, 69
[2] ON THE EQUIVALENCE OF ZERO BOUNDARY-CONDITIONS TO AN INTEGRAL CONDITION IN THE DIRICHLET PROBLEM
BOIMATOV, KK
[J]. RUSSIAN MATHEMATICAL SURVEYS, 1993, 48 (03) : 185 - 187
[3] NONLINEAR VIBRATION PROBLEM WITH NONLINEAR DIRICHLET CONDITION
HAF, H
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1973, 258 : 211 - 220
[4] A nonlinear parabolic integro-differential problem with an unknown Dirichlet boundary condition
Grimmonprez, Marijke
Slodicka, Marian
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 275 : 421 - 432
[5] SOLUTION OF THE DIRICHLET PROBLEM WITH LP BOUNDARY CONDITION
Medkova, Dagmar
[J]. KRAGUJEVAC JOURNAL OF MATHEMATICS, 2008, 31 : 29 - 42
[6] A generalized Minkowski problem with Dirichlet boundary condition
Schnürer, OC
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 355 (02) : 655 - 663
[7] A Dirichlet problem under integral boundary condition
Correa, Francisco Julio S. A.
Morbach, Joelma
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 478 (01) : 1 - 13
[8] BOUNDARY VALUE PROBLEM FOR NONLINEAR MASS-TRANSFER EQUATIONS UNDER DIRICHLET CONDITION
Saritskaia, Zhanna Yurievna
[J]. SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2022, 19 (01): : 360 - 370
[9] On a nonlinear problem with Dirichlet and Acoustic boundary conditions
Alcantara, Adriano A.
Carmo, Bruno A.
Clark, Haroldo R.
Guardia, Ronald R.
Rincon, Mauro A.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2021, 411
[10] On a nonlinear problem with Dirichlet and Acoustic boundary conditions
Alcântara, Adriano A.
Carmo, Bruno A.
Clark, Haroldo R.
Guardia, Ronald R.
Rincon, Mauro A.
[J]. Alcântara, Adriano A. (adriano.alcantara@ppgi.ufrj.br), 1600, Elsevier Inc. (411):

← 1 2 3 4 5 →