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.

scholarly journals On a fractional-order p-Laplacian boundary value problem at resonance on the half-line with two dimensional kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
O. F. Imaga ◽  
S. A. Iyase
Keyword(s):  
Differential Operator ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Half Line ◽  
At Resonance ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Problem At Resonance

AbstractIn this work, we consider the solvability of a fractional-order p-Laplacian boundary value problem on the half-line where the fractional differential operator is nonlinear and has a kernel dimension equal to two. Due to the nonlinearity of the fractional differential operator, the Ge and Ren extension of Mawhin’s coincidence degree theory is applied to obtain existence results for the boundary value problem at resonance. Two examples are used to validate the established results.

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.

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.

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