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Nonlinear functional analysis is a central subject of mathematics with applications in many areas of geometry, analysis, fl uid and elastic mechanics, physics, chemistry, biology, control theory, optimization, game theory, economics etc. This work is devoted, in a self-contained way, to several subjects of this topic such as theory of accretive operators in Banach spaces, theory of abstract Cauchy problem, metric and topological fixed point theory. Special emphasis is given to the study how these theories can be used to obtain existence and uniqueness of solutions for several types of evolution and stationary equations. In particular, equations arising in dynamical population and neutron transport equations are discussed.
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Partial differential equations --- Boundary value problems --- Fredholm operators --- Partial differential equations, Elliptic --- Partial differential equations, Nonlinear --- Topological degree --- Degree, Topological --- Degree (Topology) --- Degree theory --- Algebraic topology --- Operators, Fredholm --- Linear operators --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Boundary value problems. --- Differential equations, Partial --- Équations aux dérivées partielles --- Fredholm, Opérateurs de --- Problèmes aux limites --- Differential equations, Elliptic --- Differential equations, Nonlinear --- Nonlinear differential equations --- Nonlinear theories --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Differential equations, Linear --- Équations aux dérivées partielles. --- Fredholm, Opérateurs de. --- Problèmes aux limites.
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