scholarly journals On a Nonlocal Boundary Value Problem for Second Order Linear Ordinary Differential Equations

1995 ◽  
Vol 193 (3) ◽  
pp. 889-908 ◽  
Author(s):  
A. Lomtatidze
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Second Order ◽  
Nonlocal Boundary Value Problem ◽  
Order Linear ◽  
Linear Ordinary Differential Equations

A boundary value problem on the whole line to second order nonlinear differential equations

2010 ◽  
Vol 17 (2) ◽  
pp. 373-390
Author(s):  
Christos G. Philos ◽  
Ioannis K. Purnaras
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Nonlinear Differential Equations ◽  
Boundary Value ◽  
Second Order ◽  
Nonlinear Ordinary Differential Equations ◽  
Specific Class ◽  
Uniqueness Of Solutions ◽  
Linear Ordinary Differential Equations

Abstract Second order nonlinear ordinary differential equations are considered, and a certain boundary value problem on the whole line is studied. Two theorems are obtained as main results. The first theorem is established by the use of the Schauder theorem and concerns the existence of solutions, while the second theorem is concerned with the existence and uniqueness of solutions and is derived by the Banach contraction principle. These two theorems are applied, in particular, to the specific class of second order nonlinear ordinary differential equations of Emden–Fowler type and to the special case of second order linear ordinary differential equations, respectively.

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.

Remark on zeros of solutions of second-order linear ordinary differential equations

2016 ◽  
Vol 23 (4) ◽  
pp. 571-577
Author(s):  
Monika Dosoudilová ◽  
Alexander Lomtatidze
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Nontrivial Solution ◽  
Unique Solvability ◽  
Periodic Boundary ◽  
Periodic Boundary Value Problem ◽  
Order Linear ◽  
Linear Ordinary Differential Equations ◽  
Zeros Of Solutions

AbstractAn efficient condition is established ensuring that on any interval of length ω, any nontrivial solution of the equation ${u^{\prime\prime}=p(t)u}$ has at most one zero. Based on this result, the unique solvability of a periodic boundary value problem is studied.

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