Existence and Uniqueness of Solutions for the <i>p</i>(<i>x</i>)-Laplacian Equation with Convection Term

Existence and Uniqueness of Solutions for the <i>p</i>(<i>x</i>)-Laplacian Equation with Convection Term

In this paper, we consider the existence and uniqueness of solutions for a quasilinear elliptic equation with a variable exponent and a reaction term depending on the gradient. Based on the surjectivity result for pseudomonotone operators, we prove the existence of at least one weak solution of such...

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Bibliographic Details
Main Authors: Bin-Sheng Wang, Gang-Ling Hou, Bin Ge
Format: Article
Language:English
Published: MDPI AG 2020-10-01
Series:Mathematics
Subjects:
p(x)-Laplacian equation
convection term
pseudomonotone operators
existence results
uniqueness
Online Access:https://www.mdpi.com/2227-7390/8/10/1768
Description
Summary:In this paper, we consider the existence and uniqueness of solutions for a quasilinear elliptic equation with a variable exponent and a reaction term depending on the gradient. Based on the surjectivity result for pseudomonotone operators, we prove the existence of at least one weak solution of such a problem. Furthermore, we obtain the uniqueness of the solution for the above problem under some considerations. Our results generalize and improve the existing results.
ISSN:2227-7390

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