# Periodic solutions for quasilinear vector differential equations with maximal monotone terms

Nikolaos C. Kourogenis; Nikolaos S. Papageorgiou

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1997)

- Volume: 17, Issue: 1-2, page 67-81
- ISSN: 1509-9407

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topNikolaos C. Kourogenis, and Nikolaos S. Papageorgiou. "Periodic solutions for quasilinear vector differential equations with maximal monotone terms." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 17.1-2 (1997): 67-81. <http://eudml.org/doc/275847>.

@article{NikolaosC1997,

abstract = {We consider a quasilinear vector differential equation with maximal monotone term and periodic boundary conditions. Approximating the maximal monotone operator with its Yosida approximation, we introduce an auxiliary problem which we solve using techniques from the theory of nonlinear monotone operators and the Leray-Schauder principle. To obtain a solution of the original problem we pass to the limit as the parameter λ > 0 of the Yosida approximation tends to zero.},

author = {Nikolaos C. Kourogenis, Nikolaos S. Papageorgiou},

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

keywords = {Maximal monotone operator; coercive operator; surjective operator; demiclosed graph; Yosida approximation; compact operator; Leray-Schauder principle; fixed point; demicontinuous operator; quasilinear vector differential equations; maximal monotone operator; nonlinear monotone operators},

language = {eng},

number = {1-2},

pages = {67-81},

title = {Periodic solutions for quasilinear vector differential equations with maximal monotone terms},

url = {http://eudml.org/doc/275847},

volume = {17},

year = {1997},

}

TY - JOUR

AU - Nikolaos C. Kourogenis

AU - Nikolaos S. Papageorgiou

TI - Periodic solutions for quasilinear vector differential equations with maximal monotone terms

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 1997

VL - 17

IS - 1-2

SP - 67

EP - 81

AB - We consider a quasilinear vector differential equation with maximal monotone term and periodic boundary conditions. Approximating the maximal monotone operator with its Yosida approximation, we introduce an auxiliary problem which we solve using techniques from the theory of nonlinear monotone operators and the Leray-Schauder principle. To obtain a solution of the original problem we pass to the limit as the parameter λ > 0 of the Yosida approximation tends to zero.

LA - eng

KW - Maximal monotone operator; coercive operator; surjective operator; demiclosed graph; Yosida approximation; compact operator; Leray-Schauder principle; fixed point; demicontinuous operator; quasilinear vector differential equations; maximal monotone operator; nonlinear monotone operators

UR - http://eudml.org/doc/275847

ER -

## References

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