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

Autorzy
Seria
Rozprawy Matematyczne tom/nr w serii: 294 wydano: 1990
Zawartość
Warianty tytułu
Abstrakty
EN

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.
FR

TABLE DES MATIÈRES
1. Introduction...............................................................................................................5
2. Notation ....................................................................................................................7
3. Factorisation fredholmienne et les applications A-propres........................................8
4. Exemples des applications A-propres - applications des types monotones.............10
5. Propriétés des applications A-propres....................................................................28
6. Applications L-condensantes..................................................................................32
7. Applications aux problèmes de coïncidence............................................................45
8. Théorie du degré de coïncidence...........................................................................56
9. Application au système d'équations d'ondes semilinéaires.....................................61
Références.................................................................................................................65
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Seria
Rozprawy Matematyczne tom/nr w serii: 294
Liczba stron
67
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCXCIV
Daty
wydano
1990
Twórcy
autor
Bibliografia
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