An upper-lower solution method for the eigenvalue problem of Hadamard-type singular fractional differential equation
Xinguang Zhang, Dezhou Kong, Hui Tian, Yonghong Wu, Benchawan Wiwatanapataphee
Abstract
In this paper, we are concerned with the eigenvalue problem of Hadamard-type singular fractional differential equations with multi-point boundary conditions. By constructing the upper and lower solutions of the eigenvalue problem and using the properties of the Green function, the eigenvalue interval of the problem is established via Schauder’s fixed point theorem. The main contribution of this work is on tackling the nonlinearity which possesses singularity on some space variables.
Topics & Concepts
MathematicsEigenvalues and eigenvectorsHadamard transformSingularityMathematical analysisHadamard three-lines theoremFixed-point theoremType (biology)Interval (graph theory)Schauder fixed point theoremBoundary value problemSingular solutionDifferential equationApplied mathematicsCombinatoricsHadamard matrixPicard–Lindelöf theoremEcologyBiologyPhysicsQuantum mechanicsNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsDifferential Equations and Numerical Methods