Higher Order Boundary Value Problems on Unbounded Domains (Trends in Abstract and Applied Analysis)

✍ Scribed by Minhos Feliz Manuel Et Al

• Publisher: World Scientific Publishing Company
• Year: 2017
• Tongue: English
• Leaves: 217
• Category: Library

✦ Synopsis

This volume provides a comprehensive overview on different types of higher order boundary value problems defined on the half-line or on the real line (Sturm-Liouville and Lidstone types, impulsive, functional and problems defined by Hammerstein integral equations). It also includes classical and new methods and techniques to deal with the lack of compactness of the related operators.

The reader will find a selection of original and recent results in this field, conditions to obtain solutions with particular qualitative properties, such as homoclinic and heteroclinic solutions and its relation with the solutions of Lidstone problems on all the real line.

Each chapter contains applications to real phenomena, to classical equations or problems, with a common denominator: they are defined on unbounded intervals and the existing results in the literature are scarce or proven only numerically in discrete cases.

The last part features some higher order functional problems, which generalize the classical two-point or multi-point boundary conditions, to more comprehensive data where an overall behavior of the unknown functions and their derivatives is involved.

✦ Table of Contents

Cover
Half Title
TRENDS IN ABSTRACT AND APPLIED ANALYSIS
Series
Title Page
Copyright © 2018
Contents
Preface
Introduction
Part I
Boundary Value Problems
on the Half-Line
1: Third-Order Boundary
Value Problems
2: General nth-Order Problems
3: Impulsive Problems on the Half-Line
with Infinite Impulse Moments
Part II
Homoclinic Solutions
and Lidstone Problems
4: Homoclinic Solutions
for Second-Order Problems
5: Homoclinic Solutions
to Fourth-Order Problems
6: Lidstone Boundary Value Problems
Part III
Heteroclinic Solutions and
Hammerstein Equations
7: Heteroclinic Solutions
for Semi-linear Problems (i)
8: Heteroclinic Solutions for Semi-linear
Problems (ii)
9: Heteroclinic Solutions for Semi-linear
Problems (iii)
10: Hammerstein Integral Equations
with Sign-Changing Kernels
Part IV
Functional Boundary
Value Problems
11: Second-Order Functional Problems
12: Third-Order Functional Problems
13: ϕ-Laplacian
Equations with Functional Boundary Conditions
Bibliography
Index