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

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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.

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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. <i>Electronic Journal of Differential Equations, 2017</i>(188), pp. 1-17.

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Attribution 4.0 International

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