scholarly journals Periodic solutions for semi-linear evolution inclusions

2007 ◽  
Vol 331 (2) ◽  
pp. 1246-1262 ◽  
Author(s):  
Xiaoping Xue ◽  
Jinfeng Yu
Keyword(s):  
Periodic Solutions ◽  
Evolution Inclusions ◽  
Linear Evolution

PERIODIC SOLUTIONS FOR EVOLUTION INCLUSIONS WITH TIME-DEPENDENT SUBDIFFERENTIALS

2002 ◽  
Vol 35 (3) ◽  
Author(s):  
Nikolaos Matzakos ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Periodic Solutions ◽  
Time Dependent ◽  
Evolution Inclusions

Anti-periodic solutions for nonlinear evolution inclusions

2018 ◽  
Vol 18 (2) ◽  
pp. 1025-1047
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Periodic Solutions ◽  
Nonlinear Evolution ◽  
Evolution Inclusions

scholarly journals Extremal solutions and strong relaxation for nonlinear periodic evolution inclusions

2000 ◽  
Vol 43 (3) ◽  
pp. 569-586 ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Nikolaos Yannakakis
Keyword(s):  
Periodic Solutions ◽  
Nonlinear Operator ◽  
Periodic Problem ◽  
Distributed Parameter ◽  
Pseudomonotone Operators ◽  
Evolution Inclusions ◽  
Evolution Triple ◽  
Relaxation Theorem ◽  
Strong Relaxation ◽  
Surjectivity Result

AbstractWe study the existence of extremal periodic solutions for nonlinear evolution inclusions defined on an evolution triple of spaces and with the nonlinear operator establish A being time-dependent and pseudomonotone. Using techniques of multivalued analysis and a surjectivity result for L-generalized pseudomonotone operators, we prove the existence of extremal periodic solutions. Subsequently, by assuming that A(t, ·) is monotone, we prove a strong relaxation theorem for the periodic problem. Two examples of nonlinear distributed parameter systems illustrate the applicability of our results.

scholarly journals Existence of anti-periodic solutions for a class of first order evolution inclusions

Filomat ◽  
2014 ◽  
Vol 28 (6) ◽  
pp. 1167-1180 ◽  
Author(s):  
Xiaoyou Liu ◽  
Yiliang Liu
Keyword(s):  
Periodic Solutions ◽  
Nonlinear Evolution ◽  
Maximal Monotone ◽  
Pseudomonotone Operators ◽  
Evolution Inclusions ◽  
Derivative Operator ◽  
Evolution Triple ◽  
First Order ◽  
Nonlinear Parabolic ◽  
Surjectivity Result

The existence of anti-periodic solutions for a class of first order nonlinear evolution inclusions defined in the framework of an evolution triple of spaces is considered. We study the problems under both convexity and nonconvexity conditions on the multivalued right-hand side. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions, the surjectivity result for L-pseudomonotone operators and continuous extreme selection results from multivalued analysis. An example of a nonlinear parabolic problem is given to illustrate our results.

Existence of solutions and periodic solutions for nonlinear evolution inclusions

1999 ◽  
Vol 48 (2) ◽  
pp. 341-364 ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Francesca Papalini ◽  
Francesca Renzacci
Keyword(s):  
Periodic Solutions ◽  
Existence Of Solutions ◽  
Nonlinear Evolution ◽  
Evolution Inclusions

Time-periodic solutions to semilinear parabolic equations

1986 ◽  
Vol 104 (3-4) ◽  
pp. 329-342 ◽  
Author(s):  
Peter Grindrod ◽  
Bryan P. Rynne
Keyword(s):  
Periodic Solutions ◽  
Parabolic Equations ◽  
Evolution Equations ◽  
Periodic Forcing ◽  
Linear Diffusion ◽  
Linear Evolution ◽  
Time Periodic Solutions ◽  
Semilinear Parabolic ◽  
Time Periodic ◽  
Linear Evolution Equations

SynopsisWe consider a class of non-linear evolution equations subject to a periodic forcing term. Using bifurcation theory we obtain results on the existence and number of periodic solutions. The theory applies to semi-linear diffusion equations defined on bounded or unbounded domains.

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