Existence of Solution for Four-Point Boundary Value Problems of Second-Order Impulsive Differential Equations (II)
نویسنده
چکیده
In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using leray-Schauder theory: ⎧⎨ ⎩ x′′(t) = f(t, x(t), x′(t)), t ∈ [0, 1], t = tk, k = 1, 2,··· ,m Δx(tk) = Ik(x(tk)), k = 1, 2,··· ,m Δx′(tk) = Ik(x(tk), x ′(tk)), k = 1, 2,··· ,m x′(0) = αx′(ξ), x(1) = βx(η), (E) where 0 < ξ ≤ η < 1, α ≥ 0, β ≥ 0 and α = 1, β = 1, also αβ = 0 implies α = β, f ∈ C[J × R, R], Ik ∈ C[R,R], Ik ∈ C[R, R], J = [0, 1]. We also give a corresponding example to demonstrate our results. Keywords—impulsive differential equations, impulsive integraldifferential equation, boundary value problems
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