带有 $p$-Laplacian 算子的分数阶非线性积分边值问题的唯一正解与和算子方法

Abstract

Abstract:

This paper investigates the existence of unique positive solution for a class of fractional boundary value problems involving the $p$-Laplacian operator, a fractional derivative term in the nonlinearity $f$ and nonlinear integral terms in the boundary conditions. By constructing appropriate auxiliary boundary value problems and equivalence classes on cone, and using the theory of cone and the method of sum operators, some sufficient conditions for the existence of unique positive solution are obtained, in addition, a monotone iterative sequence uniformly converging to the unique positive solution is constructed. Finally, an example is given to illustrate the main result.

Key words: Fractional differential equation, Boundary value problem, $p$-Laplacian operator, Positive solution, Cone

CLC Number:

O175.8

Wang Wenxia. The Method of Sum Operator and Unique Positive Solution for Fractional Nonlinear Integral Boundary Value Problems with $p$-Laplacian Operator[J].Acta mathematica scientia,Series A, 2023, 43(6): 1731-1743.

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The Method of Sum Operator and Unique Positive Solution for Fractional Nonlinear Integral Boundary Value Problems with $p$-Laplacian Operator

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