Existence of extremal periodic solutions for nonlinear evolution inclusions

Nikolaos S. Papageorgiou; Nikolaos Yannakakis

Archivum Mathematicum (2001)

  • Volume: 037, Issue: 1, page 9-23
  • ISSN: 0044-8753

Abstract

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We consider a nonlinear evolution inclusion defined in the abstract framework of an evolution triple of spaces and we look for extremal periodic solutions. The nonlinear operator is only pseudomonotone coercive. Our approach is based on techniques of multivalued analysis and on the theory of operators of monotone-type. An example of a parabolic distributed parameter system is also presented.

How to cite

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Papageorgiou, Nikolaos S., and Yannakakis, Nikolaos. "Existence of extremal periodic solutions for nonlinear evolution inclusions." Archivum Mathematicum 037.1 (2001): 9-23. <http://eudml.org/doc/248748>.

@article{Papageorgiou2001,
abstract = {We consider a nonlinear evolution inclusion defined in the abstract framework of an evolution triple of spaces and we look for extremal periodic solutions. The nonlinear operator is only pseudomonotone coercive. Our approach is based on techniques of multivalued analysis and on the theory of operators of monotone-type. An example of a parabolic distributed parameter system is also presented.},
author = {Papageorgiou, Nikolaos S., Yannakakis, Nikolaos},
journal = {Archivum Mathematicum},
keywords = {evolution triple; compact embedding; exremal solution; measurable multifunction; pseudomonotone map; Kadec-Klee property; parabolic equation; p-Laplacian; evolution triple; compact embedding; extremal solution; measurable multifunction; pseudomonotone map},
language = {eng},
number = {1},
pages = {9-23},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Existence of extremal periodic solutions for nonlinear evolution inclusions},
url = {http://eudml.org/doc/248748},
volume = {037},
year = {2001},
}

TY - JOUR
AU - Papageorgiou, Nikolaos S.
AU - Yannakakis, Nikolaos
TI - Existence of extremal periodic solutions for nonlinear evolution inclusions
JO - Archivum Mathematicum
PY - 2001
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 037
IS - 1
SP - 9
EP - 23
AB - We consider a nonlinear evolution inclusion defined in the abstract framework of an evolution triple of spaces and we look for extremal periodic solutions. The nonlinear operator is only pseudomonotone coercive. Our approach is based on techniques of multivalued analysis and on the theory of operators of monotone-type. An example of a parabolic distributed parameter system is also presented.
LA - eng
KW - evolution triple; compact embedding; exremal solution; measurable multifunction; pseudomonotone map; Kadec-Klee property; parabolic equation; p-Laplacian; evolution triple; compact embedding; extremal solution; measurable multifunction; pseudomonotone map
UR - http://eudml.org/doc/248748
ER -

References

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  4. Kandilakis D., Papageorgiou N.S., Periodic solutions for nonlinear evolution inclusions, Arch. Math.(Brno) 32 (1996), 195–209. (1996) Zbl0908.34043MR1421856
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  7. Lions J.-L., Quelques Méthodes de Résolution des Problèmes aux Limites Non-Lineaires, Dunod, Paris (1969). (1969) Zbl0189.40603MR0259693
  8. Papageorgiou N.S., On the existence of solutions for nonlinear parabolic problems with discontinuities, J. Math. Anal. Appl. 205 (1997), 434-453. (1997) MR1428358
  9. Papageorgiou N.S., Papalini F., Renzacci F., Existence of solutions and periodic solutions for nonlinear evolution inclusions, Rend. Circ. Mat. Palermo, II. Ser. 48, No. 2 (1999), 341–364. (1999) Zbl0931.34043MR1692926
  10. Vrabie I., Periodic solutions for nonlinear evolution equations in a Banach space, Proc. Amer. Math. Soc. 109 (1990), 653–661. (1990) Zbl0701.34074MR1015686
  11. Zeidler E., Nonlinear Functional Analysis and its Applications II, Springer Verlag, New York (1990). (1990) Zbl0684.47029MR0816732

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