Periodic and boundary value problems for second order differential equations
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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*Correspondence: [email protected] 1Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, 10520, Thailand 2Centre of Excellence in Mathematics, CHE, Sri Ayutthaya Road, Bangkok, 10400, Thailand Full list of author information is available at the end of the article Abstract This paper is concerned with the existence of extremal solution...
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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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ژورنال
عنوان ژورنال: Proceedings Mathematical Sciences
سال: 2001
ISSN: 0253-4142,0973-7685
DOI: 10.1007/bf02829543