Existence results for a coupled system of nonlinear fractional multi-point boundary value problems at resonance

This paper aims to investigate a class of fractional multi-point boundary value problems at resonance on an infinite interval. New existence results are obtained for the given problem using Mawhin’s coincidence degree theory. Moreover, two examples are given to illustrate the main results.

Download Full-text

Existence theorems for a second orderm-point boundary value problem at resonance

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171295000901 ◽

1995 ◽

Vol 18 (4) ◽

pp. 705-710 ◽

Cited By ~ 41

Author(s):

Chaitan P. Gupta

Keyword(s):

Boundary Value Problem ◽

Boundary Value Problems ◽

Existence Theorems ◽

Boundary Value ◽

Continuation Theorem ◽

Point Boundary ◽

Existence Of A Solution ◽

At Resonance ◽

Problem At Resonance

Letf:[0,1]×R2→Rbe function satisfying Caratheodory's conditions ande(t)∈L1[0,1]. Letη∈(0,1),ξi∈(0,1),ai≥0,i=1,2,…,m−2, with∑i=1m−2ai=1,0<ξ1<ξ2<…<ξm−2<1be given. This paper is concerned with the problem of existence of a solution for the following boundary value problemsx″(t)=f(t,x(t),x′(t))+e(t),0<t<1,x′(0)=0,x(1)=x(η),x″(t)=f(t,x(t),x′(t))+e(t),0<t<1,x′(0)=0,x(1)=∑i=1m−2aix(ξi).Conditions for the existence of a solution for the above boundary value problems are given using Leray Schauder Continuation theorem.

Download Full-text

Solvability of functional differential equations with multi-point boundary value problems at resonance

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2007.10.015 ◽

2008 ◽

Vol 55 (11) ◽

pp. 2653-2661 ◽

Cited By ~ 10

Author(s):

Zengji Du

Keyword(s):

Differential Equations ◽

Boundary Value Problems ◽

Boundary Value ◽

Functional Differential Equations ◽

Point Boundary ◽

At Resonance ◽

Functional Differential

Download Full-text

Existence results for a second order nonlocal boundary value problem at resonance

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/012.2016.53.1.1328 ◽

2016 ◽

Vol 53 (1) ◽

pp. 42-52

Author(s):

Katarzyna Szymańska-Dȩbowska

Keyword(s):

Boundary Value Problem ◽

Boundary Value Problems ◽

Existence Of Solutions ◽

Boundary Value ◽

Nonlocal Boundary ◽

Existence Results ◽

Function Of Bounded Variation ◽

Nonlocal Boundary Value Problem ◽

At Resonance ◽

Problem At Resonance

The paper focuses on existence of solutions of a system of nonlocal resonant boundary value problems , where f : [0, 1] × ℝk → ℝk is continuous and g : [0, 1] → ℝk is a function of bounded variation. Imposing on the function f the following condition: the limit limλ→∞f(t, λ a) exists uniformly in a ∈ Sk−1, we have shown that the problem has at least one solution.

Download Full-text