Periodic boundary value problems for second-order functional differential equations with impulse
نویسندگان
چکیده
منابع مشابه
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...
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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...
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We deal with the nonlinear impulsive periodic boundary value problem u′′ = f (t,u,u′), u(ti+) = Ji(u(ti)), u′(ti+) = Mi(u′(ti)), i= 1,2, . . . ,m, u(0) = u(T), u′(0) = u′(T). We establish the existence results which rely on the presence of a well-ordered pair (σ1,σ2) of lower/upper functions (σ1 ≤ σ2 on [0,T]) associated with the problem. In contrast to previous papers investigating such proble...
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ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2014
ISSN: 1687-1847
DOI: 10.1186/1687-1847-2014-134