CONTENTSIntroduction......................................................................................................5I. Preliminaries1. Strong convergence and weak convergence in Banach spaces..................72. Compact and weakly compact sets in Banach spaces.................................73. Weakly compact sets in the space of integrable functions...........................84. Compact sets in the space of continuous functions.....................................95. Basic integral and differential inequalities..................................................10II. Multi-valued mappings1. Upper semi-continuous, compact and weakly compact mappings..............122. L-compact mappings..................................................................................143. Caratheodory conditions for convex-valued mappings...............................174. Convex-valued, weakly compact selectors.................................................195. Compact convex-valued vector fields.........................................................20III. Multi-valued boundary value problems1. The degree of the boundary value problem...............................................212. Existence theorems....................................................................................23IV. Boundary value problems for ordinary differential equations1. Admissible boundary value problems associated with problem (IV.1).........272. Existence theorems....................................................................................293. First order problems...................................................................................314. Second order problems..............................................................................34V. Boundary value problems for some hyperbolic partial differential equations1. Multi-valued Darboux problem....................................................................362. A multi-valued problem with nonlinear boundary conditions.......................38VI. Boundary value problems for elliptic partial differential equations1. Basic function spaces................................................................................402. The general boundary value problem........................................................41References ...................................................................................................44
@book{bwmeta1.element.zamlynska-f757319c-e33d-4e48-8592-120c10707573,
author = {Tadeusz Pruszko},
title = {Some applications of the topological degree theory to multi-valued boundary value problems},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1984},
zbl = {0543.34008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-f757319c-e33d-4e48-8592-120c10707573}
}
Tadeusz Pruszko. Some applications of the topological degree theory to multi-valued boundary value problems. GDML_Books (1984), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-f757319c-e33d-4e48-8592-120c10707573/