𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Positive solutions for mixed problems of singular fractional differential equations

✍ Scribed by Ravi P. Agarwal; Donal O'Regan; Svatoslav Staněk

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
169 KB
Volume
285
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We investigate the existence of positive solutions to the singular fractional boundary value problem: \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$^c\hspace{-1.0pt}D^{\alpha }u +f(t,u,u^{\prime },^c\hspace{-2.0pt}D^{\mu }u)=0$\end{document}, u′(0) = 0, u(1) = 0, where 1 < α < 2, 0 < μ < 1, f is a L^q^‐Carathéodory function, \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$q > \frac{1}{\alpha -1}$\end{document}, and f(t, x, y, z) may be singular at the value 0 of its space variables x, y, z. Here \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$^c \hspace{-1.0pt}D$\end{document} stands for the Caputo fractional derivative. The results are based on combining regularization and sequential techniques with a fixed point theorem on cones.

📜 SIMILAR VOLUMES

Positive Solutions of Semilinear Differe
Positive Solutions of Semilinear Differential Equations with Singularities
✍ Kunquan Lan; Jeffrey R.L. Webb 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 266 KB

The existence of positive solutions of a second order differential equation of the form z"+ g(t) f (z)=0 (1.1) with suitable boundary conditions has proved to be important in theory and applications whether g is continuous in [0, 1] or g has singularities. These equations often arise in the study

On the Existence of Positive Solutions o
On the Existence of Positive Solutions of a Singular Nonlinear Differential Equation
✍ S. Masmoudi; N. Yazidi 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 112 KB

We consider the nonlinear singular differential equation where µ and σ are two positive Radon measures on 0 ω not charging points. For a regular function f and under some hypotheses on A, we prove the existence of an infinite number of nonnegative solutions. Our approach is based on the use of the

Multiple solutions of boundary-value pro
Multiple solutions of boundary-value problems for impulsive differential equations
✍ Weibing Wang; Xuxin Yang 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 149 KB 👁 1 views

In this paper, we investigate the existence of multiple solutions to a second-order Dirichlet boundary-value problem with impulsive effects. The proof is based on critical point theorems.