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Article

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

1
College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China
2
College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(10), 1768; https://doi.org/10.3390/math8101768
Received: 7 September 2020 / Revised: 4 October 2020 / Accepted: 9 October 2020 / Published: 13 October 2020
(This article belongs to the Special Issue Advances in Nonlinear Spectral Theory)
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. View Full-Text
Keywords: p(x)-Laplacian equation; convection term; pseudomonotone operators; existence results; uniqueness p(x)-Laplacian equation; convection term; pseudomonotone operators; existence results; uniqueness
MDPI and ACS Style

Wang, B.-S.; Hou, G.-L.; Ge, B. Existence and Uniqueness of Solutions for the p(x)-Laplacian Equation with Convection Term. Mathematics 2020, 8, 1768. https://doi.org/10.3390/math8101768

AMA Style

Wang B-S, Hou G-L, Ge B. Existence and Uniqueness of Solutions for the p(x)-Laplacian Equation with Convection Term. Mathematics. 2020; 8(10):1768. https://doi.org/10.3390/math8101768

Chicago/Turabian Style

Wang, Bin-Sheng, Gang-Ling Hou, and Bin Ge. 2020. "Existence and Uniqueness of Solutions for the p(x)-Laplacian Equation with Convection Term" Mathematics 8, no. 10: 1768. https://doi.org/10.3390/math8101768

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