Résolution des équations semilinéaires avec la partie linéaire à noyau de dimension infinie via des applications A-propres
Wiesław Krawcewicz
GDML_Books, (1990), p.

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

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. (ML), (ML)+, (SL) or (SL)+) 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.

EUDML-ID : urn:eudml:doc:268429 
@book{bwmeta1.element.zamlynska-ce95cab7-4aa2-4e7e-aadc-86b5e054019f,
     author = {Wies\l aw Krawcewicz},
     title = {R\'esolution des \'equations semilin\'eaires avec la partie lin\'eaire \`a noyau de dimension infinie via des applications A-propres},
     series = {GDML\_Books},
     publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
     address = {Warszawa},
     year = {1990},
     zbl = {0722.47053},
     language = {fra},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-ce95cab7-4aa2-4e7e-aadc-86b5e054019f}
}

Wiesław Krawcewicz. Résolution des équations semilinéaires avec la partie linéaire à noyau de dimension infinie via des applications A-propres. GDML_Books (1990),  http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-ce95cab7-4aa2-4e7e-aadc-86b5e054019f/