# Representation of the set of mild solutions to the relaxed semilinear differential inclusion

Irene Benedetti; Elena Panasenko

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2006)

- Volume: 26, Issue: 1, page 143-158
- ISSN: 1509-9407

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topIrene Benedetti, and Elena Panasenko. "Representation of the set of mild solutions to the relaxed semilinear differential inclusion." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 26.1 (2006): 143-158. <http://eudml.org/doc/271136>.

@article{IreneBenedetti2006,

abstract = {We study the relation between the solutions set to a perturbed semilinear differential inclusion with nonconvex and non-Lipschitz right-hand side in a Banach space and the solutions set to the relaxed problem corresponding to the original one. We find the conditions under which the set of solutions for the relaxed problem coincides with the intersection of closures (in the space of continuous functions) of sets of δ-solutions to the original problem.},

author = {Irene Benedetti, Elena Panasenko},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {differential inclusion; mild solution; quasi-solution; convexified and perturbed problem; relaxation theorem; convexified problem; perturbation},

language = {eng},

number = {1},

pages = {143-158},

title = {Representation of the set of mild solutions to the relaxed semilinear differential inclusion},

url = {http://eudml.org/doc/271136},

volume = {26},

year = {2006},

}

TY - JOUR

AU - Irene Benedetti

AU - Elena Panasenko

TI - Representation of the set of mild solutions to the relaxed semilinear differential inclusion

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2006

VL - 26

IS - 1

SP - 143

EP - 158

AB - We study the relation between the solutions set to a perturbed semilinear differential inclusion with nonconvex and non-Lipschitz right-hand side in a Banach space and the solutions set to the relaxed problem corresponding to the original one. We find the conditions under which the set of solutions for the relaxed problem coincides with the intersection of closures (in the space of continuous functions) of sets of δ-solutions to the original problem.

LA - eng

KW - differential inclusion; mild solution; quasi-solution; convexified and perturbed problem; relaxation theorem; convexified problem; perturbation

UR - http://eudml.org/doc/271136

ER -

## References

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