scholarly journals Asymptotic analysis of oscillating parametric integrals and ordinary boundary value problems at resonance

2006 ◽  
Vol 313 (1) ◽  
pp. 218-233 ◽  
Author(s):  
A. Cañada ◽  
D. Ruiz
Keyword(s):  
Asymptotic Analysis ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
At Resonance ◽  
Parametric Integrals

scholarly journals Existence of solutions for functional boundary value problems at resonance on the half-line

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Bingzhi Sun ◽  
Weihua Jiang
Keyword(s):  
Boundary Value Problems ◽  
Banach Spaces ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Half Line ◽  
Projection Scheme ◽  
At Resonance ◽  
Functional Boundary

Abstract By defining the Banach spaces endowed with the appropriate norm, constructing a suitable projection scheme, and using the coincidence degree theory due to Mawhin, we study the existence of solutions for functional boundary value problems at resonance on the half-line with $\operatorname{dim}\operatorname{Ker}L = 1$ dim Ker L = 1 . And an example is given to show that our result here is valid.

scholarly journals Existence and uniqueness criteria for the higher-order Hilfer fractional boundary value problems at resonance

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yousef Gholami
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Higher Order ◽  
Coupled Systems ◽  
At Resonance ◽  
Uniqueness Criteria ◽  
Fractional Boundary Value Problems

Abstract This investigation is devoted to the study of a certain class of coupled systems of higher-order Hilfer fractional boundary value problems at resonance. Combining the coincidence degree theory with the Lipschitz-type continuity conditions on nonlinearities, we present some existence and uniqueness criteria. Finally, to practically implement the obtained theoretical criteria, we give an illustrative application.

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.

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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