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Existence of a Solution For a Nonlinear Degenerate Elliptic Equation Having Natural Growth Terms

Volume 7, Number 2 (2016), 26 - 38

Existence of a Solution For a Nonlinear Degenerate Elliptic Equation Having Natural Growth Terms

Communicated By: 
Enrique Zuazua
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Abstract

In this work we are interested in the existence of a solution of the nonlinear degenerate elliptic equations $Lu(x) + H(x,u,{\nabla}u)\, {\omega} = T$ in the setting of the weighted Sobolev spaces, where $H$ is a nonlinear term with natural growth with respect to ${\nabla}u$ and $T\, {\in}\,[W_0^{1,p}(\Omega , \omega)]^* = W^{-1,p^{\prime}}(\Omega,\omega)$.