Numerical-analytic method for the investigation of multipoint boundary-value problems for systems of differential equations with transformed argument

1998 ◽  
Vol 50 (11) ◽  
pp. 1805-1810
Author(s):  
M. P. Filipchuk ◽  
Ya. I. Bigun
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Analytic Method ◽  
Multipoint Boundary ◽  
Systems Of Differential Equations ◽  
Multipoint Boundary Value Problems

Nonlinear Multipoint Boundary Value Problems for Second Order Differential Equations

2010 ◽  
Vol 53 (3) ◽  
pp. 475-490
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
Deviating Arguments ◽  
Multipoint Boundary ◽  
Monotone Iterative ◽  
Second Order Differential Equations ◽  
Multipoint Boundary Value Problems

AbstractIn this paper we shall discuss nonlinear multipoint boundary value problems for second order differential equations when deviating arguments depend on the unknown solution. Sufficient conditions under which such problems have extremal and quasi-solutions are given. The problem of when a unique solution exists is also investigated. To obtain existence results, a monotone iterative technique is used. Two examples are added to verify theoretical results.

scholarly journals Building Infinitely Many Solutions for Some Model of Sublinear Multipoint Boundary Value Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-4
Author(s):  
Guy Aymard Degla
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Extension Theorem ◽  
Existence Results ◽  
Infinitely Many Solutions ◽  
Qualitative Result ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problems

We show that the sublinearity hypothesis of some well-known existence results on multipoint Boundary Value Problems (in short BVPs) may allow the existence of infinitely many solutions by using Tietze extension theorem. This is a qualitative result which is of concern in Applied Analysis and can motivate more research on the conditions that ascertain the existence of multiple solutions to sublinear BVPs. The idea of the proof is of independent interest since it shows a constructive way to have ordinary differential equations with multiple solutions.

scholarly journals Positive Solutions for Multipoint Boundary Value Problems for Singular Fractional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Mohamed Jleli ◽  
Erdal Karapinar ◽  
Bessem Samet
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Coupled Fixed Point ◽  
Multipoint Boundary ◽  
Singular Fractional Differential Equations ◽  
Fractional Differential ◽  
Multipoint Boundary Value Problems

A class of nonlinear multipoint boundary value problems for singular fractional differential equations is considered. By means of a coupled fixed point theorem on ordered sets, some results on the existence and uniqueness of positive solutions are obtained.

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