On a class of functional boundary value problems for second-order functional differential equations with parameter

Periodic Boundary Value Problems for Second-Order Functional Differential Equations

Upper and lower solution method plays an important role in studying boundary value problems for nonlinear differential equations; see 1 and the references therein. Recently, many authors are devoted to extend its applications to boundary value problems of functional differential equations 2–5 . Suppose α is one upper solution or lower solution of periodic boundary value problems for second-orde...

Initial value problems for second order hybrid fuzzy differential equations

Usage of fuzzy differential equations (FDEs) is a natural way to model dynamical systems under possibilistic uncertainty. We consider second order hybrid fuzzy differentia

Boundary value problem for second-order impulsive functional differential equations

This paper discusses a kind of linear boundary value problem for a nonlinear second order impulsive functional differential equations. We establish several existence results by using the lower and upper solutions and monotone iterative techniques. An example is discussed to illustrate the efficiency of the obtained result. © 2005 Elsevier Inc. All rights reserved.

Periodic boundary value problems for second-order functional differential equations with impulse

where J = [,T], f : J×Cτ → R is a continuous function, φ ∈ Cτ (Cτ be given in Section ), τ ≥ , ρ(t) ∈ C(J , (,∞)), ut ∈ Cτ , ut(θ ) = u(t + θ ), θ ∈ [–τ , ]. Ik ∈ C(Cτ ,R),  = t < t < t < · · · < tm < tm+ = T , J ′ = (,T)\{t, . . . , tm}. u′(tk) = u′(t+ k )–u′(t– k ), u′(t+ k ) (u′(t– k )) denote the right limit (left limit) of u′(t) at t = tk , and A ∈ R = (–∞, +∞). Impulsive diffe...

The variational iteration method for a class of tenth-order boundary value differential equations