Existence of solutions for higher order multi-point boundary value problem at resonance

2006 ◽  
Vol 27 (5) ◽  
pp. 705-711 ◽  
Author(s):  
Xiao-jie Lin ◽  
Zeng-ji Du ◽  
Wei-gao Ge
Keyword(s):  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Higher Order ◽  
Point Boundary ◽  
At Resonance ◽  
Problem At Resonance

scholarly journals Solutions of a multi-point boundary value problem for higher-order differential equations at resonance (III)

2005 ◽  
Vol 36 (2) ◽  
pp. 119-130 ◽  
Author(s):  
Yuji Liu ◽  
Weigao Ge
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Higher Order ◽  
Point Boundary ◽  
At Resonance ◽  
Higher Order Differential Equations

In this paper, we are concerned with the existence of solutions of the following multi-point boundary value problem consisting of the higher-order differential equations$ x^{(n)}(t)=f(t,x(t),x'(t),\cdots,x^{(n-1)}(t))+e(t),\;\;0

scholarly journals On second order nonlocal boundary value problem at resonance

2016 ◽  
Vol 56 (1) ◽  
pp. 143-153 ◽  
Author(s):  
Katarzyna Szymańska-Dębowska
Keyword(s):  
Boundary Value Problem ◽  
Bounded Variation ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Second Order ◽  
Function Of Bounded Variation ◽  
Nonlocal Boundary Value Problem ◽  
At Resonance ◽  
Problem At Resonance

Abstract This work is devoted to the existence of solutions for a system of nonlocal resonant boundary value problem $$\matrix{{x'' = f(t,x),} \hfill & {x'(0) = 0,} \hfill & {x'(1) = {\int_0^1 {x(s)dg(s)},} }} $$ where f : [0, 1] × ℝk → ℝk is continuous and g : [0, 1] → ℝk is a function of bounded variation.

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

1995 ◽  
Vol 18 (4) ◽  
pp. 705-710 ◽  
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.

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