Unbounded solution for a fractional boundary value problem

Abstract

This paper concerns the existence of unbounded positive solutions of a fractional boundary value problem on the half line. By means of the properties of the Green function and the compression and expansion fixed point theorem (Kwong in Fixed Point Theory Appl. 2008:164537, 2008, sufficient conditions are obtained to guarantee the existence of a solution to the posed problem.

Existence of Positive Solutions for a Third-Order Multi-Point Boundary Value Problem

“…K is a non-empty closed and convex subset of X. Lemma 12 (See [5]) The operator T is completely continuous and satisfies   .…”

“…The current analysis of these problems has a great interest and many methods are used to solve such problems. Recently certain three point boundary value problems for nonlinear ordinary differential equations have been studied by many authors [1][2][3][4][5][6][7][8][9]. The literature concerning these problems is extensive and application of theorems of functional analysis has attracted more interest.…”

Solvability of a boundary value problem at resonance

“…Boundary value problems (BVP) at resonance have been studied in many papers for ordinary differential equations (Feng and Webb 1997 ; Guezane-Lakoud and Frioui 2013 ; Guezane-Lakoud and Kılıçman 2014 ; Hu and Liu 2011 ; Jiang 2011 ; Kosmatov 2010 , 2006 ; Mawhin 1972 ; Samko et al. 1993 ; Webb and Zima 2009 ; Zima and Drygas 2013 ), most of them considered the existence of solutions for the BVP at resonance making use of Mawhin coincidence degree theory (Liu and Zhao 2007 ).…”

“… 1993 ; Webb and Zima 2009 ; Zima and Drygas 2013 ), most of them considered the existence of solutions for the BVP at resonance making use of Mawhin coincidence degree theory (Liu and Zhao 2007 ). In Guezane-Lakoud and Kılıçman ( 2014 ), Han investigated the existence and multiplicity of positive solutions for the BVP at resonance by considering an equivalent non resonance perturbed problem with the same conditions. More precisely, he wrote the original problem as under the conditions and is continuous and This result has been improved by Webb et al, in Samko et al.…”

On Some Existence and Uniqueness Results for a Class of Equations of Order0<α≤1on Arbitrary Time Scales

“…The quantitative behaviour of solutions to ordinary differential equations on time scales is currently undergoing active investigations. Many authors studied the existence and the uniqueness of the solutions of initial and boundary differential equations; see [8,[10][11][12][13][14][15][16][17][18][19][20] and the references cited therein. In the papers [21][22][23][24][25], several authors were interested by the existence and uniqueness of the first-order differential equations on time scales with initial or boundary conditions using diverse techniques and conditions.…”