Upper and Lower Solution Method for a Singular Tempered Fractional Equation with a p-Laplacian Operator
Xinguang Zhang, Peng Chen, Hui Tian, Yonghong Wu
Abstract
In this paper, we consider the existence of positive solutions for a singular tempered fractional equation with a p-Laplacian operator. By constructing a pair of suitable upper and lower solutions of the problem, some new results on the existence of positive solutions for the equation including singular and nonsingular cases are established. The asymptotic behavior of the solution is also derived, which falls in between two known curves. The interesting points of this paper are that the nonlinearity of the equation may be singular in time and space variables and the corresponding operator can have a singular kernel.
Topics & Concepts
MathematicsSingular solutionInvertible matrixOperator (biology)Laplace operatorKernel (algebra)Mathematical analysisSpace (punctuation)Nonlinear systemPure mathematicsPhysicsComputer scienceBiochemistryOperating systemRepressorQuantum mechanicsTranscription factorGeneChemistryFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Boundary Problems