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

Abstract

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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.

How to cite

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Nikolaos 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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  6. [6] H.W. Knobloch, On the existence of periodic solutions for second order vector differential equations J. Diff. Equations 9 (1971), 67-85. Zbl0211.11801
  7. [7] J. Nieto, Nonlinear second-order periodic boundary value problens J. Math. Anal. Appl. 130 (1988), 22-29. Zbl0678.34022
  8. [8] P. Omari, and M. Trombetta, Remarks on the lower and upper solutions method for second and third order periodic boundary value problems Appl. Math. Comp. 50 (1992), 1-21. Zbl0760.65078
  9. [9] M.P. Pino, M. Elgueta and Manasevich, A homotopic deformation along p of a Leray-Schauder degree result and existence for (|u'|^{p-2}u')'+f(t,u) = 0,u(0) = u(T) = 0,p > 1, J. Diff. Equations 80 (1989), 1-13. 
  10. [10] E. Zeidler, Nonlinear Functional Analysis and its Applications II, Springer-Verlag, New York 1990. Zbl0684.47029

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