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2002 | 22 | 1 | 67-78
Tytuł artykułu

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

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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.
Twórcy
  • Faculty of Mathematics, University of Bucharest, Academiei 14, 70109 Bucharest, Romania
Bibliografia
  • [1] J.P. Aubin and A. Cellina, Differential Inclusions, Springer, Berlin 1984.
  • [2] A. Auslender and J. Mechler, Second order viability problems for differential inclusions, J. Math. Anal. Appl. 181 (1984), 205-218.
  • [3] H. Brezis, Analyse fonctionelle, théorie et applications, Masson, Paris 1983.
  • [4] T. Cardinali, G. Colombo, F. Papalini and M. Tosques, On a class of evolution equations without convexity, Nonlinear Anal. 28 (1996), 217-234.
  • [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.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1032
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