Existence and Uniqueness of Weak solution of $ p( x ) $- laplacian in Sobolev spaces with variable exponents in complete manifolds

Omar Benslimane; Ahmed Aberqi; Jaouad Bennouna

Existence and Uniqueness of Weak solution of $ p( x ) $- laplacian in Sobolev spaces with variable exponents in complete manifolds

Analysis of PDEs 2020-06-09 v1

Authors: Omar Benslimane , Ahmed Aberqi , Jaouad Bennouna

Abstract

The paper deals with the existence and uniqueness of a non-trivial solution to non-homogeneous $p ( x ) -$ laplacian equations, managed by non polynomial growth operator in the framework of variable exponent Sobolev spaces on Riemannian manifolds. The mountain pass Theorem is used.

Keywords

p(x)-laplacian variable exponent Sobolev spaces Riemannian manifolds weak solution mountain pass theorem

Cite

@article{arxiv.2006.04763,
  title  = {Existence and Uniqueness of Weak solution of $ p( x ) $- laplacian in Sobolev spaces with variable exponents in complete manifolds},
  author = {Omar Benslimane and Ahmed Aberqi and Jaouad Bennouna},
  journal= {arXiv preprint arXiv:2006.04763},
  year   = {2020}
}

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