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Start Over Creator Papageorgiou, Nikolaos S.

1. Extremal solutions and strong relaxation for second order multivalued boundary value problems

Creator:
Gasiński, Leszek and Papageorgiou, Nikolaos S.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
maximal monotone operator, pseudomonotone operator, Hartman condition, convex and nonconvex problems, extremal solutions, and strong relaxation
Language:
English
Description:
In this paper we study semilinear second order differential inclusions involving a multivalued maximal monotone operator. Using notions and techniques from the nonlinear operator theory and from multivalued analysis, we obtain “extremal” solutions and we prove a strong relaxation theorem.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Nonlinear boundary value problems for second order differential inclusions

Creator:
Kyritsi , Sophia Th., Matzakos, Nikolaos, and Papageorgiou, Nikolaos S.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
measurable multifunction, usc and lsc multifunction, and maximal monotone operator
Language:
English
Description:
In this paper we study two boundary value problems for second order strongly nonlinear differential inclusions involving a maximal monotone term. The first is a vector problem with Dirichlet boundary conditions and a nonlinear differential operator of the form $x\mapsto a(x,x^{\prime })^{\prime }$. In this problem the maximal monotone term is required to be defined everywhere in the state space $\mathbb{R}^N$. The second problem is a scalar problem with periodic boundary conditions and a differential operator of the form $x\mapsto (a(x)x^{\prime })^{\prime }$. In this case the maximal monotone term need not be defined everywhere, incorporating into our framework differential variational inequalities. Using techniques from multivalued analysis and from nonlinear analysis, we prove the existence of solutions for both problems under convexity and nonconvexity conditions on the multivalued right-hand side.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. On the existence of optimal controls for nonlinear infinite dimensional systems

Creator:
Fiacca, Antonella, Papageorgiou, Nikolaos S., and Papalini, Francesca
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
evolution triple, optimal control, monotone operation, hemicontinuous operator, parabolic system, and property $(Q)$
Language:
English
Description:
We consider nonlinear systems with a priori feedback. We establish the existence of admissible pairs and then we show that the Lagrange optimal control problem admits an optimal pair. As application we work out in detail two examples of optimal control problems for nonlinear parabolic partial differential equations.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Periodic problems and problems with discontinuities for nonlinear parabolic equations

Creator:
Cardinali, Tiziana and Papageorgiou, Nikolaos S.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
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, and $R_{\delta }$-set
Language:
English
Description:
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 $(CT,L^2(Z))$.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

5. Quasilinear elliptic problems with multivalued terms

Creator:
Halidias, Nikolaos and Papageorgiou, Nikolaos S.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
subdifferential, critical point, Palais-Smale condition, Mountain Pass Theorem, Saddle Point Theorem, multivalued term, Dirichlet problem, Neumann problem, p-Laplacian, and Rayleigh quotient
Language:
English
Description:
We study the quasilinear elliptic problem with multivalued terms.We consider the Dirichlet problem with a multivalued term appearing in the equation and a problem of Neumann type with a multivalued term appearing in the boundary condition. Our approach is based on Szulkin’s critical point theory for lower semicontinuous energy functionals.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public