Nonlinear Operators

Dumitru Motreanu, Viorica Venera Motreanu and Nikolaos Papageorgiou
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Dumitru Motreanu: University of Perpignan, Department of Mathematics
Viorica Venera Motreanu: Ben-Gurion University of the Negev, Department of Mathematics
Nikolaos Papageorgiou: National Technical University, Department of Mathematics

Chapter Chapter 2 in Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems, 2014, pp 15-44 from Springer

Abstract: Abstract This chapter focuses on important classes of nonlinear operators stating abstract results that offer powerful tools for establishing the existence of solutions to nonlinear equations. Specifically, they are useful in the study of nonlinear elliptic boundary value problems as demonstrated in the final three chapters of the present book. The first section of the chapter is devoted to compact operators and emphasizes the spectral properties, including the Fredholm alternative theorem. The second section treats nonlinear operators of monotone type, possibly set-valued, among which a prominent place is occupied by maximal monotone, pseudomonotone, generalized pseudomonotone, and (S +)-operators. The cases of duality maps and p-Laplacian are of high interest in the sequel. The third section contains essential results on Nemytskii operators highlighting their main continuity and differentiability properties. Comments on the material of this chapter and related literature are given in a remarks section.

Keywords: Banach Space; Compact Operator; Monotone Operator; Maximal Monotone; Monotone Type (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-9323-5_2

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DOI: 10.1007/978-1-4614-9323-5_2

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