Existence and Uniqueness of Solutions for the p(x)-Laplacian Equation with Convection Term
Binsheng Wang, Gangling Hou, Bin Ge
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.
Topics & Concepts
UniquenessTerm (time)MathematicsMathematical analysisVariable (mathematics)Applied mathematicsExponentWeak solutionElliptic curvePure mathematicsPhysicsPhilosophyLinguisticsQuantum mechanicsNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringNumerical methods in inverse problems