An eigenvalue of an anisotropic quasilinear elliptic equation with variable exponent and Neumann boundary condition

2009 ◽  
Vol 71 (10) ◽  
pp. 4507-4514 ◽  
Author(s):  
Chao Ji
Keyword(s):  
Boundary Condition ◽  
Elliptic Equation ◽  
Neumann Boundary Condition ◽  
Variable Exponent ◽  
Quasilinear Elliptic Equation ◽  
Neumann Boundary ◽  
Quasilinear Elliptic

scholarly journals EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A NEUMANN PROBLEM INVOLVING VARIABLE EXPONENT GROWTH CONDITIONS

2008 ◽  
Vol 50 (3) ◽  
pp. 565-574 ◽  
Author(s):  
MARIA-MAGDALENA BOUREANU ◽  
MIHAI MIHĂILESCU
Keyword(s):  
Boundary Condition ◽  
Elliptic Equation ◽  
Neumann Problem ◽  
Neumann Boundary Condition ◽  
Variable Exponent ◽  
Main Tool ◽  
Neumann Boundary ◽  
Growth Conditions ◽  
Linear Elliptic Equation ◽  
Existence And Multiplicity

AbstractIn this paper we study a non-linear elliptic equation involving p(x)-growth conditions and satisfying a Neumann boundary condition on a bounded domain. For that equation we establish the existence of two solutions using as a main tool an abstract linking argument due to Brézis and Nirenberg.

scholarly journals Multiple Solutions for the p(x)− Laplace Operator with Critical Growth

2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Analia Silva
Keyword(s):  
Elliptic Equation ◽  
Laplace Operator ◽  
Multiple Solutions ◽  
Variable Exponent ◽  
Quasilinear Elliptic Equation ◽  
Critical Growth ◽  
Nontrivial Solutions ◽  
Multiplicity Of Solutions ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

AbstractThe aim of this paper is to extend previous results regarding the multiplicity of solutions for quasilinear elliptic problems with critical growth to the variable exponent case. We prove, in the spirit of [4], the existence of at least three nontrivial solutions to the quasilinear elliptic equation −Δ

New solutions for critical Neumann problems in ℝ2

2017 ◽  
Vol 8 (1) ◽  
pp. 615-644
Author(s):  
Shengbing Deng ◽  
Monica Musso
Keyword(s):  
Boundary Condition ◽  
Elliptic Equation ◽  
Small Parameter ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Normal Vector ◽  
Bounded Smooth Domain ◽  
Neumann Problems ◽  
Bounded Smooth ◽  
Outer Normal Vector

Abstract We consider the elliptic equation {-\Delta u+u=0} in a bounded, smooth domain Ω in {\mathbb{R}^{2}} subject to the nonlinear Neumann boundary condition {\frac{\partial u}{\partial\nu}=\lambda ue^{u^{2}}} , where ν denotes the outer normal vector of {\partial\Omega} . Here {\lambda>0} is a small parameter. For any λ small we construct positive solutions concentrating, as {\lambda\to 0} , around points of the boundary of Ω.

scholarly journals Boundary unique continuation theorems under zero Neumann boundary conditions

2005 ◽  
Vol 72 (1) ◽  
pp. 67-85 ◽  
Author(s):  
Xiangxing Tao ◽  
Songyan Zhang
Keyword(s):  
Boundary Condition ◽  
Elliptic Equation ◽  
Boundary Conditions ◽  
Neumann Boundary Condition ◽  
Unique Continuation ◽  
Neumann Boundary ◽  
Lipschitz Domains ◽  
Singular Potentials ◽  
Order Elliptic Equation ◽  
Second Order Elliptic Equation

Let u be a solution to a second order elliptic equation with singular potentials belonging to the Kato-Fefferman-Phong's class in Lipschitz domains. We prove the boundary unique continuation theorems and the doubling properties for u2 near the boundary under the zero Neumann boundary condition.

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