Dan Pascali

• New York University

Variational inequalities can be converted into inclusions defined by a sum between a mapping of monotone type and a subdifferential. In our case, a topological approach of variational inequalities is based on a degree function for a (S)-operator F with maximal monotone perturbations T. The paper surveys some new advances on topological degree in th...

The hyperbolic A-properness on Hilbert spaces was introduced in connection with the approximation-solvability of the semilinear equation Lu+Su=f where the linear part has an infinite-dimensional kernel. Its extension to Banach spaces requires an approximation

The paper is dedicated to the centennial of two master precursors of the Romanian mathematics: Nicolae Ciorănescu and Miron Nicolescu. We survey the progress of some topics originated in their research.

We use the Leray-Schauder degree theory to obtain bifurcation results for a large class of variational inequalities modeling unilateral problems for nonlinearly elastic plates. Our purpose is to continue a previous study [C. R. Acad. Sci., Paris, Sér. I, Math. 327, No. 11, 959-964 (1998; Zbl 0931.74027)] of the first author, regarding the existence...

Related to the mountain pass lemma, recently have appeared the mountain impasse and mountain cliff theorems; this is the reason for the chosen title. It is the purpose of our research to discuss some alternatives regarding the number and the nature of solutions of semilinear operator equations by using the mountain pass strategy without the Palais-...

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Pseudomonotonicity is the basic tool in proving the existence of solutions of variational inequalities. There is a variety of algebraic and topological extensions corresponding to the solvability of the forms of generalized variational-like inequalities. An ordering of a part of these types of pseudomonotone set-valued mappings is presented.

This report compares three nonstandard spectra for semilinear operators: the asymptotic Furi-Martelli-Vignoli spectrum, the global Feng spectrum, and the local Väth phantom. Their application in proving some kind of a nonlinear Fredholm alternative is indicated.