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

Bin-Sheng Wang, Gang-Ling Hou and Bin Ge
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Bin-Sheng Wang: College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China
Gang-Ling Hou: College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China
Bin Ge: College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China

Mathematics, 2020, vol. 8, issue 10, 1-10

Abstract: 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.

Keywords: p ( x )-Laplacian equation; convection term; pseudomonotone operators; existence results; uniqueness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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