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Start Over Subject pseudomonotone operator

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 elliptic differential equations with multivalued nonlinearities

Creator:
Fiacca, Antonella, Matzakos, Nikolas, Papgeorgiou, Nikolas S., and Servadei, Raffaella
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
upper solution, lower solution, order interval, truncation function, pseudomonotone operator, coercive operator, extremal solution, Yosida approximation, nonsmooth Palais-Smale condition, critical point, and eigenvalue problem
Language:
English
Description:
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all $\mathbb{R}$. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of $\mathbb{R}$. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally, in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. 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