Periodic problems and problems with discontinuities for nonlinear parabolic equations

Tiziana Cardinali; Nikolaos S. Papageorgiou

Czechoslovak Mathematical Journal (2000)

  • Volume: 50, Issue: 3, page 467-497
  • ISSN: 0011-4642

Abstract

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In this paper we study nonlinear parabolic equations using the method of upper and lower solutions. Using truncation and penalization techniques and results from the theory of operators of monotone type, we prove the existence of a periodic solution between an upper and a lower solution. Then with some monotonicity conditions we prove the existence of extremal solutions in the order interval defined by an upper and a lower solution. Finally we consider problems with discontinuities and we show that their solution set is a compact R δ -set in ( C T , L 2 ( Z ) ) .

How to cite

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Cardinali, Tiziana, and Papageorgiou, Nikolaos S.. "Periodic problems and problems with discontinuities for nonlinear parabolic equations." Czechoslovak Mathematical Journal 50.3 (2000): 467-497. <http://eudml.org/doc/30577>.

@article{Cardinali2000,
abstract = {In this paper we study nonlinear parabolic equations using the method of upper and lower solutions. Using truncation and penalization techniques and results from the theory of operators of monotone type, we prove the existence of a periodic solution between an upper and a lower solution. Then with some monotonicity conditions we prove the existence of extremal solutions in the order interval defined by an upper and a lower solution. Finally we consider problems with discontinuities and we show that their solution set is a compact $R_\{\delta \}$-set in $(CT,L^2(Z))$.},
author = {Cardinali, Tiziana, Papageorgiou, Nikolaos S.},
journal = {Czechoslovak Mathematical Journal},
keywords = {pseudomonotone operator; $L$-pseudomonotonicity; operator of type $(S)_\{+\}$; operator of type $L$-$(S)_\{+\}$; coercive operator; surjective operator; evolution triple; compact embedding; multifunction; upper solution; lower solution; extremal solution; $R_\{\delta \}$-set; pseudomonotone operator; -pseudomonotonicity; operator of type ; operator of type -; coercive operator; surjective operator; evolution triple; compact embedding},
language = {eng},
number = {3},
pages = {467-497},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Periodic problems and problems with discontinuities for nonlinear parabolic equations},
url = {http://eudml.org/doc/30577},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Cardinali, Tiziana
AU - Papageorgiou, Nikolaos S.
TI - Periodic problems and problems with discontinuities for nonlinear parabolic equations
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 3
SP - 467
EP - 497
AB - In this paper we study nonlinear parabolic equations using the method of upper and lower solutions. Using truncation and penalization techniques and results from the theory of operators of monotone type, we prove the existence of a periodic solution between an upper and a lower solution. Then with some monotonicity conditions we prove the existence of extremal solutions in the order interval defined by an upper and a lower solution. Finally we consider problems with discontinuities and we show that their solution set is a compact $R_{\delta }$-set in $(CT,L^2(Z))$.
LA - eng
KW - pseudomonotone operator; $L$-pseudomonotonicity; operator of type $(S)_{+}$; operator of type $L$-$(S)_{+}$; coercive operator; surjective operator; evolution triple; compact embedding; multifunction; upper solution; lower solution; extremal solution; $R_{\delta }$-set; pseudomonotone operator; -pseudomonotonicity; operator of type ; operator of type -; coercive operator; surjective operator; evolution triple; compact embedding
UR - http://eudml.org/doc/30577
ER -

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