scholarly journals On four-point boundary value problems for differential inclusions and differential equations with and without multivalued moving constraints

2012 ◽  
Vol 62 (1) ◽  
pp. 139-154 ◽  
Author(s):  
Adel Mahmoud Gomaa
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Differential Inclusions ◽  
Boundary Value ◽  
Point Boundary

ON THE SOLUTION SETS OF FOUR-POINT BOUNDARY VALUE PROBLEMS FOR NONCONVEX DIFFERENTIAL INCLUSIONS

2011 ◽  
Vol 08 (01) ◽  
pp. 23-37 ◽  
Author(s):  
ADEL MAHMOUD GOMAA
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Differential Inclusions ◽  
Boundary Value ◽  
Point Boundary ◽  
Boundary Problems ◽  
Solution Sets ◽  
Nonempty Compact ◽  
Nonconvex Differential Inclusions

We consider the multivalued problem [Formula: see text] under four boundary conditions u(0) = x0, u(η) = u(θ) = u(T) where 0 < η < θ < T and for F is a multifunctions from [0, T] × ℝn × ℝn to the nonempty compact subsets of ℝn not necessary convex. We give a lemma which is useful in the study of four boundary problems for the differential equations and the differential inclusions. Further we have results that improve earlier theorems.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

Sign in / Sign up

Export Citation Format

Share Document