Some applications of the topological degree theory to multi-valued boundary value problems

Tadeusz Pruszko. Some applications of the topological degree theory to multi-valued boundary value problems. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1984. <http://eudml.org/doc/268432>.

@book{TadeuszPruszko1984,
abstract = {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},
author = {Tadeusz Pruszko},
keywords = {Leray-Schauder topological degree technique; applications; Floquet boundary value problem; Picard boundary value problem; second order equations; Darboux problem; hyperbolic equations; elliptic equations},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Some applications of the topological degree theory to multi-valued boundary value problems},
url = {http://eudml.org/doc/268432},
year = {1984},
}

TY - BOOK
AU - Tadeusz Pruszko
TI - Some applications of the topological degree theory to multi-valued boundary value problems
PY - 1984
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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
LA - eng
KW - Leray-Schauder topological degree technique; applications; Floquet boundary value problem; Picard boundary value problem; second order equations; Darboux problem; hyperbolic equations; elliptic equations
UR - http://eudml.org/doc/268432
ER -