Erbe, L.; Krawcewicz, W. Existence of solutions to boundary value problems for impulsive second order differential inclusions. (English) Zbl 0784.34012 Rocky Mt. J. Math. 22, No. 2, 519-539 (1992). The authors consider a second order differential inclusion \(y''\in F(t,y,y')\) subject to a set of nonlinear boundary constraints \[ y(t_ k^ +)= l_ k(y(t_ k)) \qquad y'(t_ k^ +)= N_ k(y(t_ k),y'(t_ k)) \] where \(l_ k\) are given homeomorphisms and \(N_ k\) are continuous, moreover \[ G_ i(y(a_ 0),y'(a_ 0), y(a_ 1),y'(a_ 1)), \quad i=1,2 \] where \(a_ 0=t_ 0<t_ 1<\cdots <t_ m<t_{m+1}=a_ 1\). Their main existence result, Theorem 2.2, is proved by means of the topological transversality method of Granas based on the existence of a priori bounds for the solutions of the above boundary value problem which is suitably modified to deal with the impulsive nature of the problem. Two motivating examples involving impulses are presented. Reviewer: P.Zezza (Firenze) Cited in 22 Documents MSC: 34A60 Ordinary differential inclusions 34A37 Ordinary differential equations with impulses 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:second order differential inclusion; nonlinear boundary constraints; topological transversality method of Granas; boundary value problem; impulses × Cite Format Result Cite Review PDF Full Text: DOI