ArticleOriginal scientific text
Title
On the existence of viable solutions for a class of second order differential inclusions
Authors 1
Affiliations
- Faculty of Mathematics, University of Bucharest, Academiei 14, 70109 Bucharest, Romania
Abstract
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
Keywords
viable solutions, ϕ-monotone operators, differential inclusions
Bibliography
- J.P. Aubin and A. Cellina, Differential Inclusions, Springer, Berlin 1984.
- A. Auslender and J. Mechler, Second order viability problems for differential inclusions, J. Math. Anal. Appl. 181 (1984), 205-218.
- H. Brezis, Analyse fonctionelle, théorie et applications, Masson, Paris 1983.
- T. Cardinali, G. Colombo, F. Papalini and M. Tosques, On a class of evolution equations without convexity, Nonlinear Anal. 28 (1996), 217-234.
- A. Cernea, Existence of viable solutions for a class of nonconvex differential inclusions, J. Convex Anal., submitted.
- B. Cornet and B. Haddad, Théoreme de viabilité pour inclusions differentielles du second order, Israel J. Math. 57 (1987), 225-238.
- M. Degiovanni, A. Marino and M. Tosques, Evolution equations with lack of convexity, Nonlinear Anal. 9 (1995), 1401-1443.
- T.X.D. Ha and M. Marques, Nonconvex second order differential inclusions with memory, Set-valued Anal. 5 (1995), 71-86.
- V. Lupulescu, Existence of solutions to a class of second order differential inclusions, Cadernos de Matematica, Aveiro Univ., CM01/I-11.
- L. Marco and J.A. Murillo, Viability theorems for higher-order differential inclusions, Set-valued Anal. 6 (1998), 21-37.
- M. Tosques, Quasi-autonomus parabolic evolution equations associated with a class of non linear operators, Ricerche Mat. 38 (1989), 63-92.
Pages:
67-78
Main language of publication
English
Received
2002-02-20
Published
2002
DOI: 10.7151/dmgt.1032
Exact and natural sciences