scholarly journals Existence results for a fourth order multipoint boundary value problem at resonance

2015 ◽  
Vol 34 (3) ◽  
pp. 259-266 ◽  
Author(s):  
S.A. Iyase
Keyword(s):  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Existence Results ◽  
Multipoint Boundary ◽  
At Resonance ◽  
Problem At Resonance ◽  
Multipoint Boundary Value Problem

scholarly journals On a Singular Second-Order Multipoint Boundary Value Problem at Resonance

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
S. A. Iyase ◽  
O. F. Imaga
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Existence Results ◽  
Second Order ◽  
Multipoint Boundary ◽  
At Resonance ◽  
Problem At Resonance ◽  
Multipoint Boundary Value Problem

The aim of this paper is to derive existence results for a second-order singular multipoint boundary value problem at resonance using coincidence degree arguments.

scholarly journals Solvability of a Third-Order Multipoint Boundary Value Problem at Resonance

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Zengji Du ◽  
Bensheng Zhao ◽  
Zhanbing Bai
Keyword(s):  
Boundary Value Problem ◽  
Existence Result ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Third Order ◽  
Multipoint Boundary ◽  
At Resonance ◽  
Problem At Resonance ◽  
Multipoint Boundary Value Problem

We discuss a third-order multipoint boundary value problem under some appropriate resonance conditions. By using the coincidence degree theory, we establish the existence result of solutions. The emphasis here is that the dimension of the linear operator is equal to two. Our results supplement other results.

scholarly journals A symmetric solution of a multipoint boundary value problem at resonance

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
Nickolai Kosmatov
Keyword(s):  
Boundary Value Problem ◽  
Symmetric Solution ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Multipoint Boundary ◽  
At Resonance ◽  
Carathéodory Conditions ◽  
Problem At Resonance ◽  
Coincidence Degree Theorem ◽  
Multipoint Boundary Value Problem

We apply a coincidence degree theorem of Mawhin to show the existence of at least one symmetric solution of the nonlinear second-order multipoint boundary value problemu″(t)=f(t,u(t),|u′(t)|),t∈(0,1),u(0)=∑i=1nμiu(ξi),u(1−t)=u(t),t∈[0,1], where0<ξ1<ξ2<…<ξn≤1/2,∑i=1nμi=1,f:[0,1]×ℝ2→ℝwithf(t,x,y)=f(1−t,x,y),(t,x,y)∈[0,1]×ℝ2, satisfying the Carathéodory conditions.

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

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.

scholarly journals On a Fourth-Order Boundary Value Problem at Resonance

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Man Xu ◽  
Ruyun Ma
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Elastic Beam ◽  
First Eigenvalue ◽  
At Resonance ◽  
Problem At Resonance ◽  
Spectrum Structure

We investigate the spectrum structure of the eigenvalue problem u4x=λux,  x∈0,1;  u0=u1=u′0=u′1=0. As for the application of the spectrum structure, we show the existence of solutions of the fourth-order boundary value problem at resonance -u4x+λ1ux+gx,ux=hx,  x∈0,1;  u0=u1=u′0=u′1=0, which models a statically elastic beam with both end-points being cantilevered or fixed, where λ1 is the first eigenvalue of the corresponding eigenvalue problem and nonlinearity g may be unbounded.

scholarly journals Existence of Positive Solutions for a Nonlinear Higher-Order Multipoint Boundary Value Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Min Zhao ◽  
Yongping Sun
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Higher Order ◽  
Existence Results ◽  
Monotone Iterative Method ◽  
Multipoint Boundary ◽  
Monotone Iterative ◽  
Existence Of Positive Solutions ◽  
Multipoint Boundary Value Problem

We study the existence of positive solutions for a nonlinear higher-order multipoint boundary value problem. By applying a monotone iterative method, some existence results of positive solutions are obtained. The main result is illustrated with an example.

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