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Filippov Lemma for certain differential inclusion of third order

100%

Bartuzel G. , Fryszkowski A.

tom Vol. 41, nr 2

337-352

We propose a version of the Filippov Lemma for differential inclusions of the type y'" + k2y' is an element of F(x,y) defined on [—1,1] with boundary conditions y(-1)=y(1)=y'(1)=0.

BVP for Caratheodory inclusions in Hilbert spaces: sharp existence conditions and applications

84%

Benedetti I. , Panasenko E. , Taddei V.

tom Vol. 16, nr 2

237-258

This article concerns an existence result for Floquet boundary value problems associated to semilinear differential inclusions with Carathéodory right hand side in a Hilbert space. We apply a continuation principle and we require a sharp (i.e., localized on the boundary) transversality condition. We give an application to a nonlinear partial differential inclusion with periodic conditions.

The dynamic response of an elastic background under undetermined variable loads

84%

Ossowski A.

2008

tom Vol. 23

309--314

The problem of Lagrange stability of an elastic background excited by undetermined variable loads is considered. A discrete model of the background with bounded excitations is studied. Applying optimal Lyapunov functions, upper bounds on the dynamic response of the background are estimated and interpreted in terms of rough sets. The described approach is useful to estimate vibration transmission in ground as well as to analyze vibration of a road surface or rail-track loaded by moving vehicles.