On a fixed point theorem and applications to a two point boundary value problem
Existence and uniqueness of the solution to a fourth order nonlinear vector periodic boundary value problem is proved by using the estimates for derivatives of the Green function for the corresponding homogenous scalar problem
A criterion for the unique solvability of and sufficient conditions for the correctness of the modified Vallèe-Poussin problem are established for the linear ordinary differential equations with singularities.
We consider a boundary value problem for first order nonconvex differential inclusion and we obtain some existence results by using the set-valued contraction principle.
The periodic boundary value problem u''(t) = f(t,u(t),u'(t)) with u(0) = u(2π) and u'(0) = u'(2π) is studied using the generalized method of upper and lower solutions, where f is a Carathéodory function satisfying a Nagumo condition. The existence of solutions is obtained under suitable conditions on f. The results improve and generalize the work of M.-X. Wang et al. [5].
This paper investigates a class of fractional functional integrodifferential inclusions with nonlocal conditions in Banach spaces. The existence of mild solutions of these inclusions is determined under mixed continuity and Carathéodory conditions by using strongly continuous operator semigroups and Bohnenblust-Karlin's fixed point theorem.