Unbounded Solutions of a Boundary Value Problem for Abstract nth-Order Differential Equations on an Infinite Interval

Unbounded Solutions of a Boundary Value Problem for Abstract nth-Order Differential Equations on an Infinite Interval

The existence of unbounded nonnegative solutions of a boundary value problem for nth-order differential equations defined on an infinite interval is obtained by means of the M ¨ onch fixed-point theorem. An example is then presented to demonstrate the application of our results.

On a Multipoint Boundary Value Problem for a Fractional Order Differential Inclusion on an Infinite Interval

1 Department of Mathematics, Faculty of Sciences, Razi University, Kermanshah 67149, Iran 2Department of Mathematics and Computer Sciences, Faculty of Art and Sciences, Cankaya University, 06530 Ankara, Turkey 3 Institute of Space Sciences, P.O. BOX MG-23, 76900 Magurele, Bucharest, Romania 4Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O...

Existence of Unbounded Solutions for a Third-Order Boundary Value Problem on Infinite Intervals

On boundary value problem for fractional differential equations

In this paper‎, ‎we study the existence of solutions for a‎ ‎ fractional boundary value problem‎. ‎By using critical point theory‎ ‎ and variational methods‎, ‎we give some new criteria to guarantee‎ ‎ that‎ ‎ the problems have at least one solution and infinitely many solutions.

On boundary value problems of higher order abstract fractional integro-differential equations

The aim of this paper is to establish the existence of solutions of boundary value problems of nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques such as fractional calculus, H"{o}lder inequality, Krasnoselskii's fixed point theorem and nonlinear alternative of Leray-Schauder type. Examples are exhibited to illustrate the main resu...