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Noncompact perturbation of nonconvex noncompact sweeping process with delay

Mohammed S. Abdo, Ahmed G. Ibrahim, Satish K. Panchal (2020)

Commentationes Mathematicae Universitatis Carolinae

We prove an existence theorem of solutions for a nonconvex sweeping process with nonconvex noncompact perturbation in Hilbert space. We do not assume that the values of the orient field are compact.

Nonlinear boundary value problems for differential inclusions y'' ∈ F(t,y,y')

L. H. Erbe, W. Krawcewicz (1991)

Annales Polonici Mathematici

Applying the topological transversality method of Granas and the a priori bounds technique we prove some existence results for systems of differential inclusions of the form y'' ∈ F(t,y,y'), where F is a Carathéodory multifunction and y satisfies some nonlinear boundary conditions.

Nonlinear boundary value problems for second order differential inclusions

Sophia Th. Kyritsi, Nikolaos M. Matzakos, Nikolaos S. Papageorgiou (2005)

Czechoslovak Mathematical Journal

In this paper we study two boundary value problems for second order strongly nonlinear differential inclusions involving a maximal monotone term. The first is a vector problem with Dirichlet boundary conditions and a nonlinear differential operator of the form x a ( x , x ' ) ' . In this problem the maximal monotone term is required to be defined everywhere in the state space N . The second problem is a scalar problem with periodic boundary conditions and a differential operator of the form x ( a ( x ) x ' ) ' . In this case the maximal...

Nonlinear eigenvalue problems for fourth order ordinary differential equations

Jolanta Przybycin (1995)

Annales Polonici Mathematici

This paper was inspired by the works of Chiappinelli ([3]) and Schmitt and Smith ([7]). We study the problem ℒu = λau + f(·,u,u',u'',u''') with separated boundary conditions on [0,π], where ℒ is a composition of two operators of Sturm-Liouville type. We assume that the nonlinear perturbation f satisfies the inequality |f(x,u,u',u'',u''')| ≤ M|u|. Because of the presence of f the considered equation does not in general have a linearization about 0. For this reason the global bifurcation theorem of...

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