Positive solutions for superlinear Riemann-Liouville fractional boundary-value problems

Date

2017-10-04

Authors

Bachar, Imed
Maagli, Habib
Radulescu, Vicentiu

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

Using a perturbation argument, we establish the existence and uniqueness of a positive continuous solution for the following superlinear Riemann-Liouville fractional boundary-value problem Dαu(x) - u(x)ϕ(x, u(x)) = 0, 0 < x < 1, u(0) = u'(0) = limx→0+ x4-α u″(x) = 0, u″(1) = α > 0, where 3 < α ≤ 4 and ϕ(x, t) satisfies a suitable integrability condition.

Description

Keywords

Fractional differential equation, Positive solution, Green's function, Perturbation, Schauder fixed point theorem

Citation

Bachar, I., Mâagli, H., & Radulescu, V. D. (2017). Positive solutions for superlinear Riemann-Liouville fractional boundary-value problems. <i>Electronic Journal of Differential Equations, 2017</i>(240), pp. 1-16.

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Attribution 4.0 International

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