Tiziana Cardinali, Lucia Santori (2011)
Commentationes Mathematicae Universitatis Carolinae
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In this paper we prove two existence theorems for abstract boundary value problems controlled by semilinear evolution inclusions in which the nonlinear part is a lower Scorza-Dragoni multifunction. Then, by using these results, we obtain the existence of periodic mild solutions.
Tiziana Cardinali, Nikolaos S. Papageorgiou (2000)
Czechoslovak Mathematical Journal
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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...
Nikolaos S. Papageorgiou, Nikolaos Yannakakis (2002)
Archivum Mathematicum
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In this paper we consider a periodic problem driven by the one dimensional -Laplacian and with a discontinuous right hand side. We pass to a multivalued problem, by filling in the gaps at the discontinuity points. Then for the multivalued problem, using the nonsmooth critical point theory, we establish the existence of at least three distinct periodic solutions.