On the existence of viable solutions for a class of second order differential inclusions

• Autorzy: Aurelian Cernea
• Języki publikacji: EN

Abstrakty

EN

We prove the existence of viable solutions to the Cauchy problem x'' ∈ F(x,x'), x(0) = x₀, x'(0) = y₀, where F is a set-valued map defined on a locally compact set $M ⊂ R^{2n}$, contained in the Fréchet subdifferential of a ϕ-convex function of order two.

Słowa kluczowe

EN

viable solutions; ϕ-monotone operators; differential inclusions

Kategorie tematyczne

• 34A60: Differential inclusions

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2002
• Tom: 22
• Numer: 1
• Strony: 67-78

Daty

wydano

2002

otrzymano

2002-02-20

Twórcy

autor

Aurelian Cernea

• Faculty of Mathematics, University of Bucharest, Academiei 14, 70109 Bucharest, Romania

Bibliografia

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• [3] H. Brezis, Analyse fonctionelle, théorie et applications, Masson, Paris 1983.
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• [5] A. Cernea, Existence of viable solutions for a class of nonconvex differential inclusions, J. Convex Anal., submitted.
• [6] B. Cornet and B. Haddad, Théoreme de viabilité pour inclusions differentielles du second order, Israel J. Math. 57 (1987), 225-238.
• [7] M. Degiovanni, A. Marino and M. Tosques, Evolution equations with lack of convexity, Nonlinear Anal. 9 (1995), 1401-1443.
• [8] T.X.D. Ha and M. Marques, Nonconvex second order differential inclusions with memory, Set-valued Anal. 5 (1995), 71-86.
• [9] V. Lupulescu, Existence of solutions to a class of second order differential inclusions, Cadernos de Matematica, Aveiro Univ., CM01/I-11.
• [10] L. Marco and J.A. Murillo, Viability theorems for higher-order differential inclusions, Set-valued Anal. 6 (1998), 21-37.
• [11] M. Tosques, Quasi-autonomus parabolic evolution equations associated with a class of non linear operators, Ricerche Mat. 38 (1989), 63-92.

Identyfikatory

DOI

10.7151/dmgt.1032