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Abstract
We prove the existence of a ground state solution for the qusilinear elliptic equation in , under suitable conditions on a locally Holder continuous non-linearity , the non-linearity may exhibit a singularity as . We also prove the non-existence of radially symmetric solutions to the singular elliptic equation in , as where .
Highlights
In this paper, we are concerned with the existence of ground state solution or positive solution for the following problem div(| u |p 2 u) = f (x,u), x u > 0, x (1) u(x) = 0, xThe problem (1) appears in the study of non-Newtonian fluids [1,2] and non-Newtonian filtration [3]
We prove the existence of a ground state solution for the qusilinear elliptic equation div(| u |p 2 u)
We prove the non-existence of radially symmetric solutions to the singular elliptic equation div(| u |p 2 u) = d (x)[g(u) r(u) | u |q ], u(x) > 0 in RN, u(x) 0 as | x |, where d (x) = d (| x |) C(RN, (0, )), N
Summary
We are concerned with the existence of ground state solution or positive solution for the following problem div(| u |p 2 u) = f (x,u), x u > 0, x (1). In [20], the author extended results to the problem (1) for p = 2 where f is not necessarily separable. Motivated by papers [4,5,6,20], we extend the results to p > 1 and get two theorems. The second purpose is to give a result for nonexistence of solution. To the best of our knowledge, there has been very less result for nonexistence of solution about singular elliptic equation.
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