scholarly journals Multiplicity of Positive Solutions for a Second-Order Elliptic System of Kirchhoff Type

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
S. Khademloo ◽  
E. Valipour ◽  
A. Babakhani
Keyword(s):  
Elliptic System ◽  
Positive Solutions ◽  
Elliptic Problems ◽  
Second Order ◽  
Kirchhoff Type ◽  
Nonnegative Solutions ◽  
Variational Tools ◽  
Order Elliptic System ◽  
Multiplicity Of Positive Solutions

We study elliptic problems of Kirchhoff type inΩ⊂RN  (N≥3). Using variational tools, we establish the existence of at least two nontrivial and nonnegative solutions.

NONNEGATIVE SOLUTIONS FOR INDEFINITE SUBLINEAR ELLIPTIC PROBLEMS

2012 ◽  
Vol 14 (03) ◽  
pp. 1250021 ◽  
Author(s):  
FRANCISCO ODAIR DE PAIVA
Keyword(s):  
Bounded Domain ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Solution Method ◽  
Mountain Pass Theorem ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Nonnegative Solutions ◽  
Carathéodory Function ◽  
Multiplicity Of Positive Solutions

This paper is devoted to the study of existence, nonexistence and multiplicity of positive solutions for the semilinear elliptic problem [Formula: see text] where Ω is a bounded domain of ℝN, λ ∈ ℝ and g(x, u) is a Carathéodory function. The obtained results apply to the following classes of nonlinearities: a(x)uq + b(x)up and c(x)(1 + u)p (0 ≤ q < 1 < p). The proofs rely on the sub-super solution method and the mountain pass theorem.

scholarly journals Positive Solutions for Elliptic Problems with the Nonlinearity Containing Singularity and Hardy-Sobolev Exponents

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yong-Yi Lan ◽  
Xian Hu ◽  
Bi-Yun Tang
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Elliptic Problems ◽  
Semilinear Elliptic Equations ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic ◽  
Multiplicity Of Positive Solutions

In this paper, we study multiplicity of positive solutions for a class of semilinear elliptic equations with the nonlinearity containing singularity and Hardy-Sobolev exponents. Using variational methods, we establish the existence and multiplicity of positive solutions for the problem.

On the Dirichlet Problem for a Second Order Elliptic System with Degeneration on the Entire Domain Boundary

1999 ◽  
Vol 6 (4) ◽  
pp. 395-400
Author(s):  
M. Usanetashvili
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Elliptic System ◽  
Domain Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Entire Domain ◽  
Order Elliptic System

Abstract The solvability of the first boundary value problem is investigated for a second order elliptic system with degeneration on the entire domain boundary.

Sign in / Sign up

Export Citation Format

Share Document