Nikolaos S. Papageorgiou

Handbook of multivalued analysis

Preface. I. Evolution Inclusions Involving Monotone Coercive Operators. II. Evolution Inclusions of the Subdifferential Type. III. Special Topics in Differential and Evolution Inclusions. IV. Optimal Control. V. Calculus of Variations. VI. Mathematical Economics. VII. Stochastic Games. VIII. Special Topics in Mathematical Economics and Optimization. Appendix. References. Symbol. Index. Errata of Volume A.

An Introduction to Nonlinear Analysis: Theory

An Introduction to Nonlinear Analysis: Theory is an overview of some basic, important aspects of Nonlinear Analysis, with an emphasis on those not included in the classical treatment of the field. Today Nonlinear Analysis is a very prolific part of modern mathematical analysis, with fascinating theory and many different applications ranging from mathematical physics and engineering to social sciences and economics. Topics covered in this book include the necessary background material from topology, measure theory and functional analysis (Banach space theory). The text also deals with multivalued analysis and basic features of nonsmooth analysis, providing a solid background for the more applications-oriented material of the book An Introduction to Nonlinear Analysis: Applications by the same authors. The book is self-contained and accessible to the newcomer, complete with numerous examples, exercises and solutions. It is a valuable tool, not only for specialists in the field interested in technical details, but also for scientists entering Nonlinear Analysis in search of promising directions for research.

Nonsmooth critical point theory and nonlinear boundary value problems

MATHEMATICAL BACKGROUND Sobolev Spaces Set-Valued Analysis Nonsmooth Analysis Nonlinear Operators Elliptic Differential Equations Remarks CRITICAL POINT THEORY Locally Lipschitz Functionals Constrained Locally Lipschitz Functionals Perturbations of Locally Lipschitz Functionals Local Linking and Extensions Continuous Functionals Multivalued Functionals Remarks ORDINARY DIFFERENTIAL EQUATIONS Dirichlet Problems Periodic Problems Nonlinear Boundary Conditions Variational Methods Method of Upper and Lower Solutions Positive Solutions and Other Methods Hamiltonian Inclusions Remarks ELLIPTIC EQUATIONS Problems at Resonance Neumann Problems Problems with an Area-Type Term Strongly Nonlinear Problems Method of Upper and Lower Solutions Multiplicity Results Positive Solutions Problems with Discontinuous Nonlinearities Remarks APPENDIX Set Theory and Topology Measure Theory Functional Analysis Nonlinear Analysis List of Symbols References

Convergence theorems for Banach space valued integrable multifunctions.

In this work we generalize a result of Kato on the pointwise behavior of a P weakly convergent sequence in the Lebesgue-Bochner spaces LX(fi) (I _< p _< (R)). Then we use that result to prove Fatous type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions. Analogous con- vergence results are also proved for the sets of integrable selectors of those multifunctions. In the process of proving those convergence theorems we make some useful observations concerning the Kuratowski-Mosco convergence of sets.

On the theory of Banach space valued multifunctions. 1. Integration and conditional expectation

Banach space valued multifunctions defined on a complete [sigma]-finite measure space ([Omega], [Sigma], [mu]) are studied. Their set valued integral is defined and its properties are examined. Since the definition of the integral involves the set of integrable selectors of the multifunction, the structure of that set is also studied. Some Banach-like spaces of multifunctions are introduced and studied. Multifunctions depending on a parameter are also considered and it is examined wheter certain continuity, semicontinuity and other topological properties are preserved by set valued integration. Finally, for integrable multifunctions, the properties of their set valued conditional expectation are studied.

Random fixed point theorems for measurable multifunctions in Banach spaces

On demontre plusieurs theoremes de points fixes aleatoires pour des multifonctions mesurables fermees et non fermees satisfaisant des conditions de continuite generales

Degree theory for operators of monotone type and nonlinear elliptic equations with inequality constraints

Introduction Mathematical background Degree theoretic results Variational-hemivariational inequalities Hemivariational inequalities with an asymmetric subdifferential Bibliography.

Handbook of applied analysis

- Preface.- Smooth and Nonsmooth Calculus.- Extremal Problems and Optimal Control.- Nonlinear Operators and Fixed Points.- Critical Point Theory and Variational Methods.- Boundary Value Problems and Hamiltonian Systems.- Multivalued Analysis.- Economic Equilibrium and Optimal Economic Planning.- Game Theory.- Uncertainty, Information, Decision Making.- Evolution Equations.- References.- List of Symbols.- Index.

Multiple solutions for nonlinear Neumann problems driven by a nonhomogeneous differential operator

We consider a nonlinear Neumann problem driven by a nonhomogeneous quasilinear degenerate elliptic differential operator div a(x,∇u), a special case of which is the p-Laplacian. The reaction term is a Carathéodory function f(x, s) which exhibits subcritical growth in s. Using variational methods based on the mountain pass and second deformation theorems, together with truncation and minimization techniques, we show that the problem has three nontrivial smooth solutions, two of which have constant sign (one positive, the other negative). A crucial tool in our analysis is a result of independent interest which we prove here and which relates W 1,p and C1 local minimizers of a C1-functional constructed with the general differential operator div a(x,∇u).

Wang’s multiplicity result for superlinear (,)–equations without the Ambrosetti–Rabinowitz condition

We consider a nonlinear elliptic equation driven by the sum of a p– Laplacian and a q–Laplacian where 1 < q ≤ 2 ≤ p < ∞ with a (p − 1)– superlinear Caratheodory reaction term which doesn’t satisfy the usual Ambrosetti–Rabinowitz condition. Using variational methods based on critical point theory together with techniques from Morse theory, we show that the problem has at leat three nontrivial solutions; among them one is positive and one is negative.