Periodic solutions for nonlinear evolution inclusions

Dimitrios A. Kandilakis; Nikolaos S. Papageorgiou

Archivum Mathematicum (1996)

  • Volume: 032, Issue: 3, page 195-209
  • ISSN: 0044-8753

Abstract

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In this paper we prove the existence of periodic solutions for a class of nonlinear evolution inclusions defined in an evolution triple of spaces ( X , H , X * ) and driven by a demicontinuous pseudomonotone coercive operator and an upper semicontinuous multivalued perturbation defined on T × X with values in H . Our proof is based on a known result about the surjectivity of the sum of two operators of monotone type and on the fact that the property of pseudomonotonicity is lifted to the Nemitsky operator, which we prove in this paper.

How to cite

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Kandilakis, Dimitrios A., and Papageorgiou, Nikolaos S.. "Periodic solutions for nonlinear evolution inclusions." Archivum Mathematicum 032.3 (1996): 195-209. <http://eudml.org/doc/247864>.

@article{Kandilakis1996,
abstract = {In this paper we prove the existence of periodic solutions for a class of nonlinear evolution inclusions defined in an evolution triple of spaces $(X,H,X^\{*\})$ and driven by a demicontinuous pseudomonotone coercive operator and an upper semicontinuous multivalued perturbation defined on $T\times X$ with values in $H$. Our proof is based on a known result about the surjectivity of the sum of two operators of monotone type and on the fact that the property of pseudomonotonicity is lifted to the Nemitsky operator, which we prove in this paper.},
author = {Kandilakis, Dimitrios A., Papageorgiou, Nikolaos S.},
journal = {Archivum Mathematicum},
keywords = {evolution triple; compact embedding; pseudomonotone operator; demicontinuity; coercive operator; dominated convergence theorem; evolution triple; pseudomonotone operator; coercive operator},
language = {eng},
number = {3},
pages = {195-209},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Periodic solutions for nonlinear evolution inclusions},
url = {http://eudml.org/doc/247864},
volume = {032},
year = {1996},
}

TY - JOUR
AU - Kandilakis, Dimitrios A.
AU - Papageorgiou, Nikolaos S.
TI - Periodic solutions for nonlinear evolution inclusions
JO - Archivum Mathematicum
PY - 1996
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 032
IS - 3
SP - 195
EP - 209
AB - In this paper we prove the existence of periodic solutions for a class of nonlinear evolution inclusions defined in an evolution triple of spaces $(X,H,X^{*})$ and driven by a demicontinuous pseudomonotone coercive operator and an upper semicontinuous multivalued perturbation defined on $T\times X$ with values in $H$. Our proof is based on a known result about the surjectivity of the sum of two operators of monotone type and on the fact that the property of pseudomonotonicity is lifted to the Nemitsky operator, which we prove in this paper.
LA - eng
KW - evolution triple; compact embedding; pseudomonotone operator; demicontinuity; coercive operator; dominated convergence theorem; evolution triple; pseudomonotone operator; coercive operator
UR - http://eudml.org/doc/247864
ER -

References

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  1. Real Analysis and Probability, Academic Press, New York (1972). MR0435320
  2. Periodic solutions of semilinear equations of evolution of compact type, J. Math. Anal. Appl. 82 (1981), 33-48. Zbl0465.34014MR0626739
  3. Operateurs Maximaux Monotones, North Holland, Amsterdam (1973). Zbl0252.47055
  4. Existence of periodic solutions for nonlinear equations of evolution, Proc. Nat. Acad. Sci. USA 53 (1965), 1100-1103. Zbl0135.17601MR0177295
  5. Pseudomonotone operators and nonlinear elliptic boundary value problems on unbounded domains, Proc. Nat. Acad. Sci. USA 74 (1977), 2659-2661. MR0445124
  6. Variational methods for nondifferentiable functions and their applications to partial differential equations, J. Math. Anal. Appl. 80 (1981), 102-129. MR0614246
  7. On continuous approximations for multifunctions, Pacific J. Math. 123 (1986), 9-31. MR0834135
  8. Vector Measures, Math. Surveys, 15, AMS Providence, Rhode Island (1977). MR0453964
  9. Topics in Metric Fixed Point Theory, Cambridge Univ. Press, Cambridge (1990). MR1074005
  10. Pseudomonotonicity and the Leray-Lions condition, Differential and Integral Equations 6 (1993), 37-45. MR1190164
  11. Existence of periodic solutions for nonlinear evolution equations in Hilbert spaces, Proc. AMS 120 (1994), 185-192. Zbl0795.34051MR1174494
  12. On the existence of periodic solutions for a class of nonlinear evolution inclusions, Bolletino UMI 7-B (1993), 591-605. MR1244409
  13. Galerkin approximations for nonlinear evolution inclusions, Comm. Math. Univ. Carolinae 35 (1994), 705-720. MR1321241
  14. Quelques Methods de Resolution des Problemes aux Limites Nonlineaires, Dunod, Paris (1969). 
  15. Convergence theorems for Banach space valued integrable multifunctions, Inter. J. Math. and Math. Sci. 10 (1987), 433-464. Zbl0619.28009MR0896595
  16. On measurable multifunctions with applications to random multivalued equations, Math. Japonica 32 (1987), 437-464. Zbl0634.28005MR0914749
  17. Periodic solutions for semilinear evolution equations, Nonl. Anal. TMA 3 (1979), 221-235. 
  18. Nonlinear evolution equations in Banach spaces, Proc. AMS 109 (1990), 653-661. 
  19. Periodic solutions for nonlinear evolution equations in a Banach space, Proc. AMS 109 (1990), 653-661. Zbl0701.34074MR1015686
  20. Survey of measurable selection theorems, SIAM J. Control Opt. 15 (1977), 859-903. Zbl0427.28009MR0486391
  21. Nonlinear Functinal Analysis and its Applications, Springer-Verlag, New York (1990). 

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