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.

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.

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

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

scholarly journals Generalized Yosida Approximations Based on RelativelyA-Maximalm-Relaxed Monotonicity Frameworks

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Heng-you Lan
Keyword(s):  
Banach Space ◽  
Resolvent Operator ◽  
Evolution Equations ◽  
Maximal Monotone ◽  
Monotone Operators ◽  
Monotone Mappings ◽  
Evolution Inclusions ◽  
Inclusion Problems ◽  
First Order ◽  
New Class

We introduce and study a new notion of relativelyA-maximalm-relaxed monotonicity framework and discuss some properties of a new class of generalized relatively resolvent operator associated with the relativelyA-maximalm-relaxed monotone operator and the new generalized Yosida approximations based on relativelyA-maximalm-relaxed monotonicity framework. Furthermore, we give some remarks to show that the theory of the new generalized relatively resolvent operator and Yosida approximations associated with relativelyA-maximalm-relaxed monotone operators generalizes most of the existing notions on (relatively) maximal monotone mappings in Hilbert as well as Banach space and can be applied to study variational inclusion problems and first-order evolution equations as well as evolution inclusions.

scholarly journals Sensitivity analysis for optimal control problems governed by nonlinear evolution inclusions

2017 ◽  
Vol 6 (2) ◽  
pp. 199-235 ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Vicenţiu D. Rădulescu ◽  
Dušan D. Repovš
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Evolution ◽  
Distributed Parameter ◽  
Evolution Inclusions ◽  
Content Type ◽  
Continuity Properties ◽  
Nonlinear Parabolic ◽  
The Value Function

AbstractWe consider a nonlinear optimal control problem governed by a nonlinear evolution inclusion and depending on a parameter λ. First we examine the dynamics of the problem and establish the nonemptiness of the solution set and produce continuous selections of the solution multifunction ${\xi\mapsto S(\xi\/)}$ (ξ being the initial condition). These results are proved in a very general framework and are of independent interest as results about evolution inclusions. Then we use them to study the sensitivity properties of the optimal control problem. We show that we have Hadamard well-posedness (continuity of the value function), and we establish the continuity properties of the optimal multifunction. Finally, we present an application on a nonlinear parabolic distributed parameter system.

scholarly journals Periodic solutions of nonlinear evolution inclusions

1994 ◽  
Vol 52 (1-3) ◽  
pp. 277-286 ◽  
Author(s):  
V. Lakshmikantham ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Periodic Solutions ◽  
Nonlinear Evolution ◽  
Evolution Inclusions
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