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Existence of solutions for some quasilinear p ( x ) -elliptic problem with Hardy potential

Elhoussine AzroulMohammed BouzianiHassane HjiajAhmed Youssfi — 2019

Mathematica Bohemica

We consider the anisotropic quasilinear elliptic Dirichlet problem - i = 1 N D i a i ( x , u , u ) + | u | s ( x ) - 1 u = f + λ | u | p 0 ( x ) - 2 u | x | p 0 ( x ) in Ω , u = 0 on Ω , where Ω is an open bounded subset of N containing the origin. We show the existence of entropy solution for this equation where the data f is assumed to be in L 1 ( Ω ) and λ is a positive constant.

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