Résolution des équations semilinéaires avec la partie linéaire à noyau de dimension infinie via des applications A-propres

Wiesław Krawcewicz

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1990

Abstract

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This work is devoted to the solvability of semilinear equations(*) Lx + f(x) = y, x ∈ D(L) ⊂ E, y ∈ F,where E, F are real Banach spaces and L: D(L) → F is a linear operator with dimKerL = codimR(L) = ∞. We introduce the notion of a generalized A-proper mapping f(x) associated with the operator L and show that some classes of monotone-type mappings (i.e. ( M L ) , ( M L ) + , ( S L ) or ( S L ) + ) are nontrivial examples of A-proper mappings. Using the topological transversality, we develop the continuation method for L-condensing A-proper mappings and obtain solvability results for the equation (*). The abstract results for A-proper mappings are applied to the problem of time-periodic solutions of semilinear wave equations. We introduce a generalized coincidence degree called the Browder-Petryshyn-Mawhin coincidence degree.

How to cite

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Wiesław Krawcewicz. Résolution des équations semilinéaires avec la partie linéaire à noyau de dimension infinie via des applications A-propres. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1990. <http://eudml.org/doc/268429>.

@book{WiesławKrawcewicz1990,
abstract = {TABLE DES MATIÈRES1. Introduction...............................................................................................................52. Notation ....................................................................................................................73. Factorisation fredholmienne et les applications A-propres........................................84. Exemples des applications A-propres - applications des types monotones.............105. Propriétés des applications A-propres....................................................................286. Applications L-condensantes..................................................................................327. Applications aux problèmes de coïncidence............................................................458. Théorie du degré de coïncidence...........................................................................569. Application au système d'équations d'ondes semilinéaires.....................................61Références.................................................................................................................65},
author = {Wiesław Krawcewicz},
keywords = {semilinear equation at resonance; semi-Fredholm operator; infinite dimensional kernel; A-proper mapping; analogue of Galerkin's method; coincidence degree theory},
language = {fre},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Résolution des équations semilinéaires avec la partie linéaire à noyau de dimension infinie via des applications A-propres},
url = {http://eudml.org/doc/268429},
year = {1990},
}

TY - BOOK
AU - Wiesław Krawcewicz
TI - Résolution des équations semilinéaires avec la partie linéaire à noyau de dimension infinie via des applications A-propres
PY - 1990
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - TABLE DES MATIÈRES1. Introduction...............................................................................................................52. Notation ....................................................................................................................73. Factorisation fredholmienne et les applications A-propres........................................84. Exemples des applications A-propres - applications des types monotones.............105. Propriétés des applications A-propres....................................................................286. Applications L-condensantes..................................................................................327. Applications aux problèmes de coïncidence............................................................458. Théorie du degré de coïncidence...........................................................................569. Application au système d'équations d'ondes semilinéaires.....................................61Références.................................................................................................................65
LA - fre
KW - semilinear equation at resonance; semi-Fredholm operator; infinite dimensional kernel; A-proper mapping; analogue of Galerkin's method; coincidence degree theory
UR - http://eudml.org/doc/268429
ER -

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