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

被引：12
作者：
Wang, Bin-Sheng [1 ]
Hou, Gang-Ling [1 ]
Ge, Bin [2 ]
机构：
[1] Harbin Engn Univ, Coll Aerosp & Civil Engn, Harbin 150001, Peoples R China
[2] Harbin Engn Univ, Coll Math Sci, Harbin 150001, Peoples R China
来源：
MATHEMATICS | 2020年 / 8卷 / 10期
基金：
中国国家自然科学基金;
关键词：
p(x)-Laplacian equation; convection term; pseudomonotone operators; existence results; uniqueness; EXPONENT ELLIPTIC-EQUATIONS; VARIABLE EXPONENT; POSITIVE SOLUTIONS; GROWTH; REGULARITY; DEPENDENCE; GRADIENT; SPACES; PERTURBATION; FUNCTIONALS;
D O I：
10.3390/math8101768
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：1 / 10
页数：10
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