Linear and Nonlinear Non-Fredholm Operators: Theory and Applications

Preface
Contents
Chapter 1 Auxiliary Materials
	1.1 Functional spaces and embedding theorems
	1.2 Linear Elliptic Boundary value problems
	1.3 Superposition operators
	1.4 Pseudodifferential operators. Definitions and examples
	1.5 Linear Fredholm operators
	1.6 Fourier transform and related topics
	1.7 On the necessary conditions for preserving the nonnegative cone: double scale anomalous diffusion
	1.8 The Lippman-Schwinger equation: the generalized Fourier Transform
Chapter 2 Solvability in the sense of sequences: non-Fredholm operators
	2.1 Non-Fredholm equations with normal diffusion and drift in the whole line: scalar case
	2.2 Non-Fredholm equations in a finite interval with normal diffusion and drift: scalar case
	2.3 Non-Fredholm systems with normal diffusion and drift in the whole line
	2.4 Non-Fredholm systems in a finite interval with normal diffusion and drift
Chapter 3 Solvability of some integro-differential equations with drift and superdiffusion
	3.1 The whole real line case: scalar equation
	3.2 The problem on the finite interval: scalar equation
	3.3 The whole real line case: system case
	3.4 The problem on the finite interval: system case
Chapter 4 Existence of solutions for some non-Fredholm integro-differential equations with mixed diffusion
	4.1 Mixed-diffusion: scalar case
	4.2 Mixed-diffusion: system case
Chapter 5 Non-Fredholm Schrödinger type operators
	5.1 Solvability in the sense of sequences with two potentials
	5.2 Solvability in the sense of sequences with Laplacian and a single potential: regular case
	5.3 Solvability in the sense of sequences with Laplacian and a single potential: singular case
	5.4 Generalized Poisson type equation with a potential
References
Index