NDLI: Positive Solutions for a System of Fractional Boundary Value Problems with r-Laplacian Operators, Uncoupled Nonlocal Conditions and Positive Parameters

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Positive Solutions for a System of Fractional Boundary Value Problems with r-Laplacian Operators, Uncoupled Nonlocal Conditions and Positive Parameters

Content Provider	MDPI
Author	Tudorache, Alexandru Luca, Rodica
Copyright Year	2022
Description	In this paper, we investigate the existence and nonexistence of positive solutions for a system of Riemann–Liouville fractional differential equations with r-Laplacian operators, subject to nonlocal uncoupled boundary conditions that contain Riemann–Stieltjes integrals, various fractional derivatives and positive parameters. We first change the unknown functions such that the new boundary conditions have no positive parameters, and then, by using the corresponding Green functions, we equivalently write this new problem as a system of nonlinear integral equations. By constructing an appropriate operator $A$ , the solutions of the integral system are the fixed points of $A$ . Following some assumptions regarding the nonlinearities of the system, we show (by applying the Schauder fixed-point theorem) that operator $A$ has at least one fixed point, which is a positive solution of our problem, when the positive parameters belong to some intervals. Then, we present intervals for the parameters for which our problem has no positive solution.
Starting Page	164
e-ISSN	20751680
DOI	10.3390/axioms11040164
Journal	Axioms
Issue Number	4
Volume Number	11
Language	English
Publisher	MDPI
Publisher Date	2022-04-06
Access Restriction	Open
Subject Keyword	Axioms Mathematical Physics Riemann–liouville Fractional Differential Equations Nonlocal Boundary Conditions Positive Parameters Positive Solutions Existence Nonexistence
Content Type	Text
Resource Type	Article

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