Existence and multiplicity of solutions for anisotropic elliptic problems with variable exponent and nonlinear Robin boundary conditions Brahim Ella
Date
2017-07-24
Authors
Ellahyani, Brahim
El Hachimi, Abderrahmane
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
This article presents sufficient conditions for the existence of solutions of the anisotropic quasilinear elliptic equation with variable exponent and nonlinear Robin boundary conditions,
-ΣNi=1</sub> ∂/∂x (|∂u/∂xi|pi(x)-2 ∂u/∂xi) + ΣNi=1 |u|pi(x)-2 u + λ|u|m(x)-2 u = γg(x, u)
in Ω,
ΣNi=1 |∂u/∂xi|pi(x)-2 ∂u/∂xi vi = μ|u|q(x)-2 u on ∂Ω.
Under appropriate assumptions on the data, we prove some existence and multiplicity results. The methods are based on Mountain Pass and Fountain theorems.
Description
Keywords
Anisotropic elliptic problems, Robin boundary conditions existence and multiplicity
Citation
Ellahyani, B., & El Hachimi, A. (2017). Existence and multiplicity of solutions for anisotropic elliptic problems with variable exponent and nonlinear Robin boundary conditions Brahim Ella. Electronic Journal of Differential Equations, 2017(188), pp. 1-17.
Rights
Attribution 4.0 International