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2019 Multiple positive solutions for a coupled system of $p$-Laplacian fractional order three-point boundary value problems
S. Nageswara Rao
Rocky Mountain J. Math. 49(2): 609-626 (2019). DOI: 10.1216/RMJ-2019-49-2-609

Abstract

In this paper, we attempt to establish the existence of at least three positive solutions for a coupled system of $p$-Laplacian fractional order boundary value problems \begin{aligned}\begin{cases} D_{a^+}^{\beta _1}(\phi _{p}(D_{a^+}^{\alpha _1}u(t)))=f_1(t, u(t), v(t)) & \quad a\lt t\lt b,\\ D_{a^+}^{\beta _2}(\phi _{p}(D_{a^+}^{\alpha _2}v(t)))=f_2(t, u(t), v(t)) & \quad a\lt t\lt b, \end{cases}\end{aligned} with the boundary conditions \begin{aligned}\begin{cases} u^{(j)}(a)=0,\ j=0,1,2,\ldots , \ u{''}(b)=\delta u{''}(\xi ),\\ \phi _{p}(D_{a^+}^{\alpha _1}u(a))=0, \ \phi _{p}(D_{a^+}^{\alpha _1} u(b)) =\vartheta \phi _{p}( D_{a^+}^{\alpha _1}u(\eta )),\\ v^{(j)}(a)=0,\ j=0,1,2,\ldots , \ v{''}(b)=\delta v{''}(\xi ),\\ \phi _{p}(D_{a^+}^{\alpha _2}v(a))=0, \ \phi _{p}(D_{a^+}^{\alpha _2} v(b))=\vartheta \phi _{p}( D_{a^+}^{\alpha _2}v(\eta )), \end{cases}\end{aligned} by applying the five functional fixed point theorem.

Citation

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S. Nageswara Rao. "Multiple positive solutions for a coupled system of $p$-Laplacian fractional order three-point boundary value problems." Rocky Mountain J. Math. 49 (2) 609 - 626, 2019. https://doi.org/10.1216/RMJ-2019-49-2-609

Information

Received: 27 July 2015; Revised: 1 August 2018; Published: 2019
First available in Project Euclid: 23 June 2019

zbMATH: 07079987
MathSciNet: MR3973243
Digital Object Identifier: 10.1216/RMJ-2019-49-2-609

Subjects:
Primary: 34B10, 34B15, 34B27

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 2 • 2019
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