Existence of Nontrivial Positive Solutions to a Semilinear Elliptic System with Variable Coefficients

This paper studies the nontrivial positive solutions to a semilinear elliptic system with variable coefficients in the n dimensional Euclide space. By constructing a new variational space and using some linking theorems, this paper finally proves the existence of positive solution to a semilinear elliptic system.

Existence of Nontrivial Positive Solutions to a Semilinear Elliptic System

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.204-208.4548 ◽

2012 ◽

Vol 204-208 ◽

pp. 4548-4551

Author(s):

Da Wei Sun ◽

Gao Sheng Zhu

Keyword(s):

Positive Solution ◽

Elliptic System ◽

Positive Solutions ◽

Embedding Theorems ◽

Semilinear Elliptic ◽

This paper studies the nontrivial positive solutions to a semilinear elliptic system in the n dimensional Euclide space. By constructing new variational space, using the linking theorems and some embedding theorems, this paper proves the existence of positive solution to a semilinear elliptic system, and improves the results of Li and Wang.

NON-EXISTENCE, MONOTONICITY FOR POSITIVE SOLUTIONS OF SEMILINEAR ELLIPTIC SYSTEM IN $\mathbb{R}_+^N$

Communications in Contemporary Mathematics ◽

10.1142/s0219199710003853 ◽

2010 ◽

Vol 12 (03) ◽

pp. 351-372 ◽

Cited By ~ 3

Author(s):

YUXIA GUO

Keyword(s):

Weak Solution ◽

Elliptic System ◽

Half Space ◽

Positive Solutions ◽

Integral Inequality ◽

Existence Results ◽

Semilinear Elliptic ◽

Moving Plane ◽

Positive Weak Solution

In this paper, by using the Alexandrov–Serrin method of moving plane combined with integral inequality, we prove some non-existence results for positive weak solution of semilinear elliptic system in the half-space [Formula: see text].

The Nehari manifold approach for multiplicity of positive solutions to semilinear elliptic system involving multi-singular inverse square potentials with Sobolev critical exponent

Mathematical Sciences ◽

10.1007/s40096-017-0228-y ◽

2017 ◽

Vol 11 (4) ◽

pp. 267-273

Author(s):

A. Akhavan ◽

H. Rahimi

Keyword(s):

Critical Exponent ◽

Elliptic System ◽

Positive Solutions ◽

Nehari Manifold ◽

Semilinear Elliptic ◽

Multiplicity Of Positive Solutions ◽

The Nehari Manifold ◽

Inverse Square Potentials ◽

Sobolev Critical Exponent

Regularity results for positive solutions of a semilinear elliptic system

Annali di Matematica Pura ed Applicata (1923 -) ◽

10.1007/bf02505951 ◽

2001 ◽

Vol 179 (1) ◽

pp. 125-147

Author(s):

Antonio Boccuto ◽

Enzo Mitidieri

Keyword(s):

Elliptic System ◽

Positive Solutions ◽

Semilinear Elliptic ◽

Regularity Results

Positive Solutions to a Neumann Problem of Semilinear Elliptic System with Critical Nonlinearity

Acta Mathematicae Applicatae Sinica English Series ◽

10.1007/s10255-006-0343-2 ◽

2006 ◽

Vol 22 (4) ◽

pp. 687-702 ◽

Cited By ~ 1

Author(s):

Wei-hua Yang

Keyword(s):

Neumann Problem ◽

Elliptic System ◽

Positive Solutions ◽

Critical Nonlinearity ◽

Semilinear Elliptic ◽

Existence of entire large positive solutions of a semilinear elliptic system

Applied Mathematics and Computation ◽

10.1016/s0096-3003(03)00809-9 ◽

2004 ◽

Vol 155 (3) ◽

pp. 687-698 ◽

Cited By ~ 10

Author(s):

Yahong Peng ◽

Yongli Song

Keyword(s):

Elliptic System ◽

Positive Solutions ◽

Semilinear Elliptic ◽

A note on the existence of positive solutions for a fourth-order semilinear elliptic system

Acta Mathematica Sinica English Series ◽

10.1007/s10114-010-8042-6 ◽

2010 ◽

Vol 26 (7) ◽

pp. 1263-1276

Author(s):

Yu Xia Guo ◽

Guang Zhong Chen

Keyword(s):

Elliptic System ◽

Positive Solutions ◽

Fourth Order ◽

Semilinear Elliptic ◽

Existence Of Positive Solutions

Multiple positive solutions for a critical elliptic system with concave—convex nonlinearities

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210508000875 ◽

2009 ◽

Vol 139 (6) ◽

pp. 1163-1177 ◽

Cited By ~ 20

Author(s):

Tsing-San Hsu ◽

Huei-Li Lin

Keyword(s):

Variational Methods ◽

Elliptic System ◽

Positive Solutions ◽

Critical Growth ◽

Bounded Domains ◽

Multiple Positive Solutions ◽

Multiplicity Results ◽

Existence And Multiplicity ◽

Semilinear Elliptic ◽

We consider a semilinear elliptic system with both concave—convex nonlinearities and critical growth terms in bounded domains. The existence and multiplicity results of positive solutions are obtained by variational methods.