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

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

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

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topAurelian 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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- [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] V. Lupulescu, Existence of solutions to a class of second order differential inclusions, Cadernos de Matematica, Aveiro Univ., CM01/I-11. Zbl1096.34062
- [10] L. Marco and J.A. Murillo, Viability theorems for higher-order differential inclusions, Set-valued Anal. 6 (1998), 21-37. Zbl0926.34008
- [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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