# Near viability for fully nonlinear differential inclusions

Open Mathematics (2014)

- Volume: 12, Issue: 10, page 1447-1459
- ISSN: 2391-5455

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topIrina Căpraru, and Alina Lazu. "Near viability for fully nonlinear differential inclusions." Open Mathematics 12.10 (2014): 1447-1459. <http://eudml.org/doc/269131>.

@article{IrinaCăpraru2014,

abstract = {We consider the nonlinear differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A is an m-dissipative operator on a separable Banach space X and F is a multi-function. We establish a viability result under Lipschitz hypothesis on F, that consists in proving the existence of solutions of the differential inclusion above, starting from a given set, which remain arbitrarily close to that set, if a tangency condition holds. To this end, we establish a kind of set-valued Gronwall’s lemma and a compactness theorem, which are extensions to the nonlinear case of similar results for semilinear differential inclusions. As an application, we give an approximate null controllability result.},

author = {Irina Căpraru, Alina Lazu},

journal = {Open Mathematics},

keywords = {Nonlinear differential inclusions; A priori estimates; Near viability; viability; differential inclusion; tangency; evolution inclusion; m-dissipative; Lipschitz; compactness; control system},

language = {eng},

number = {10},

pages = {1447-1459},

title = {Near viability for fully nonlinear differential inclusions},

url = {http://eudml.org/doc/269131},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Irina Căpraru

AU - Alina Lazu

TI - Near viability for fully nonlinear differential inclusions

JO - Open Mathematics

PY - 2014

VL - 12

IS - 10

SP - 1447

EP - 1459

AB - We consider the nonlinear differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A is an m-dissipative operator on a separable Banach space X and F is a multi-function. We establish a viability result under Lipschitz hypothesis on F, that consists in proving the existence of solutions of the differential inclusion above, starting from a given set, which remain arbitrarily close to that set, if a tangency condition holds. To this end, we establish a kind of set-valued Gronwall’s lemma and a compactness theorem, which are extensions to the nonlinear case of similar results for semilinear differential inclusions. As an application, we give an approximate null controllability result.

LA - eng

KW - Nonlinear differential inclusions; A priori estimates; Near viability; viability; differential inclusion; tangency; evolution inclusion; m-dissipative; Lipschitz; compactness; control system

UR - http://eudml.org/doc/269131

ER -

## References

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