Impulsive BVPs with nonlinear boundary conditions for the second order differential equations without growth restrictions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:292

Article

Rachunková, I ; Tomecek, J

关键词: ordinary differential equation of the second order;    lower and upper functions;    nonlinear boundary value conditions;    impulses;   

DOI  :  10.1016/j.jmaa.2003.12.023

来源: Elsevier

【 摘 要 】

The paper deals with the impulsive nonlinear boundary value problem u (t) = f(t, u(t), u'(t)), {g(1)(u(a), u(b)) = 0, {g(2)(u'(a), u'(b)) = 0, {u (tj +) = Ij (u(tj)), j = 1,...,p, {u' (tj+) = Mj (u'(tj)), j = 1,...,P where J = [a, b], f is an element of Car(J x R-2), g(1), g(2) is an element of C (R-2), I-j, M-j is an element of C (R). We prove the existence of a solution to this problem under the assumption that there exist lower and upper functions associated with the problem. Our proofs are based on the Schauder fixed point theorem and on the method of a priori estimates. No growth restrictions are imposed on f, g(1), g(2), I-j, M-j. (C) 2004 Elsevier Inc. All rights reserved.

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