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

Aurelian Cernea

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2002)

  • Volume: 22, Issue: 1, page 67-78
  • ISSN: 1509-9407

Abstract

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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 2 n , contained in the Fréchet subdifferential of a ϕ-convex function of order two.

How to cite

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Aurelian Cernea. "On the existence of viable solutions for a class of second order differential inclusions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 22.1 (2002): 67-78. <http://eudml.org/doc/271534>.

@article{AurelianCernea2002,
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 $M ⊂ R^\{2n\}$, contained in the Fréchet subdifferential of a ϕ-convex function of order two.},
author = {Aurelian Cernea},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {viable solutions; ϕ-monotone operators; differential inclusions; -monotone operators},
language = {eng},
number = {1},
pages = {67-78},
title = {On the existence of viable solutions for a class of second order differential inclusions},
url = {http://eudml.org/doc/271534},
volume = {22},
year = {2002},
}

TY - JOUR
AU - Aurelian Cernea
TI - On the existence of viable solutions for a class of second order differential inclusions
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2002
VL - 22
IS - 1
SP - 67
EP - 78
AB - 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.
LA - eng
KW - viable solutions; ϕ-monotone operators; differential inclusions; -monotone operators
UR - http://eudml.org/doc/271534
ER -

References

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  1. [1] J.P. Aubin and A. Cellina, Differential Inclusions, Springer, Berlin 1984. 
  2. [2] A. Auslender and J. Mechler, Second order viability problems for differential inclusions, J. Math. Anal. Appl. 181 (1984), 205-218. Zbl0808.34012
  3. [3] H. Brezis, Analyse fonctionelle, théorie et applications, Masson, Paris 1983. 
  4. [4] T. Cardinali, G. Colombo, F. Papalini and M. Tosques, On a class of evolution equations without convexity, Nonlinear Anal. 28 (1996), 217-234. Zbl0880.47045
  5. [5] A. Cernea, Existence of viable solutions for a class of nonconvex differential inclusions, J. Convex Anal., submitted. Zbl1077.34018
  6. [6] B. Cornet and B. Haddad, Théoreme de viabilité pour inclusions differentielles du second order, Israel J. Math. 57 (1987), 225-238. Zbl0659.34012
  7. [7] M. Degiovanni, A. Marino and M. Tosques, Evolution equations with lack of convexity, Nonlinear Anal. 9 (1995), 1401-1443. Zbl0545.46029
  8. [8] T.X.D. Ha and M. Marques, Nonconvex second order differential inclusions with memory, Set-valued Anal. 5 (1995), 71-86. Zbl0824.34020
  9. [9] V. Lupulescu, Existence of solutions to a class of second order differential inclusions, Cadernos de Matematica, Aveiro Univ., CM01/I-11. Zbl1096.34062
  10. [10] L. Marco and J.A. Murillo, Viability theorems for higher-order differential inclusions, Set-valued Anal. 6 (1998), 21-37. Zbl0926.34008
  11. [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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