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Singular perturbations for systems of differential inclusions

100%

Quincampoix M.

Banach Center Publications

1995

tom 32

nr 1

341-348

We study a system of two differential inclusions such that there is a singular perturbation in the second one. We state new convergence results of solutions under assumptions concerning contingent derivative of the perturbed inclusion. These results state that there exists at least one family of solutions which converges to some solution of the reduced system. We extend this result to perturbed systems with state constraints.

Equilibria and strict equilibria of multivalued maps on noninvariant sets

51%

Cardaliaguet P., Gabor G., Quincampoix M.

Annales Polonici Mathematici

2003

tom 82

nr 1

19-37

This paper is concerned with existence of equilibrium of a set-valued map in a given compact subset of a finite-dimensional space. Previously known conditions ensuring existence of equilibrium imply that the set is either invariant or viable for the differential inclusion generated by the set-valued map. We obtain some equilibrium existence results with conditions which imply neither invariance nor viability of the given set. The problem of existence of strict equilibria is also discussed.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Banach Center Publications

2 Quincampoix M.

1 Cardaliaguet P.

1 Gabor G.

1 2003

1 1995

Wyniki wyszukiwania

Singular perturbations for systems of differential inclusions

Equilibria and strict equilibria of multivalued maps on noninvariant sets