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. Electronic Journal of Differential Equations, 2017(240), pp. 1-16.
Rights
Attribution 4.0 International