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Near viability for fully nonlinear differential inclusions

100%

Căpraru I., Lazu A.

Open Mathematics

2014

tom 12

nr 10

1447-1459

We consider the nonlinear differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A is an m-dissipative operator on a separable Banach space X and F is a multi-function. We establish a viability result under Lipschitz hypothesis on F, that consists in proving the existence of solutions of the differential inclusion above, starting from a given set, which remain arbitrarily close to that set, if a tangency condition holds. To this end, we establish a kind of set-valued Gronwall’s lemma and a compactness theorem, which are extensions to the nonlinear case of similar results for semilinear differential inclusions. As an application, we give an approximate null controllability result.

Positive periodic solutions of parabolic evolution problems: a translation along trajectories approach

76%

Ćwiszewski A.

Open Mathematics

2011

tom 9

nr 2

244-268

A translation along trajectories approach together with averaging procedure and topological degree are used to derive effective criteria for existence of periodic solutions for nonautonomous evolution equations with periodic perturbations. It is shown that a topologically nontrivial zero of the averaged right hand side is a source of periodic solutions for the equations with increased frequencies. Our setting involves equations on closed convex cones, therefore it enables us to study positive solutions of nonlinear parabolic partial differential equations.

Ograniczanie wyników

2 Open Mathematics

1 Căpraru I.

1 Lazu A.

1 Ćwiszewski A.

1 2014

1 2011

Wyniki wyszukiwania

Near viability for fully nonlinear differential inclusions

Positive periodic solutions of parabolic evolution problems: a translation along trajectories approach