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 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.

Quasilinearization and boundary value problems at resonance

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Kareem Alanazi ◽  
Meshal Alshammari ◽  
Paul Eloe
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Approximate Solutions ◽  
Monotonicity Condition ◽  
Uniqueness Of Solutions ◽  
Shift Method ◽  
At Resonance ◽  
Problem At Resonance

Abstract A quasilinearization algorithm is developed for boundary value problems at resonance. To do so, a standard monotonicity condition is assumed to obtain the uniqueness of solutions for the boundary value problem at resonance. Then the method of upper and lower solutions and the shift method are applied to obtain the existence of solutions. A quasilinearization algorithm is developed and sequences of approximate solutions are constructed, which converge monotonically and quadratically to the unique solution of the boundary value problem at resonance. Two examples are provided in which explicit upper and lower solutions are exhibited.

scholarly journals Higher Order Nonlocal Boundary Value Problems at Resonance on the Half-line

2020 ◽  
Vol 13 (1) ◽  
pp. 33-47
Author(s):  
Samuel Iyase ◽  
Abiodun Opanuga
Keyword(s):  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Higher Order ◽  
Half Line ◽  
Index Zero ◽  
Nonlocal Boundary Value Problems ◽  
At Resonance ◽  
Fredholm Map

This paper investigates the solvability of a class of higher order nonlocal boundaryvalue problems of the formu(n)(t) = g(t, u(t), u0(t)· · · u(n−1)(t)), a.e. t ∈ (0, ∞)subject to the boundary conditionsu(n−1)(0) = (n − 1)!ξn−1u(ξ), u(i)(0) = 0, i = 1, 2, . . . , n − 2,u(n−1)(∞) = Z ξ0u(n−1)(s)dA(s)where ξ > 0, g : [0, ∞) × <n −→ < is a Caratheodory’s function,A : [0, ξ] −→ [0, 1) is a non-decreasing function with A(0) = 0, A(ξ) = 1. The differential operatoris a Fredholm map of index zero and non-invertible. We shall employ coicidence degree argumentsand construct suitable operators to establish existence of solutions for the above higher ordernonlocal boundary value problems at resonance.

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