Higher Order Boundary Value Problems on Unbounded Domains

The following sections are included:

• Contents
• Preface
• Introduction

Sturm–Liouville theory was initiated by Jacques Charles François Sturm (1803–1855) and Joseph Liouville (1809–1882) to study second-order linear differential equations of the form

The following sections are included:

• Introduction
• Definitions and auxiliary results
• Existence and localization result
• Example

The following sections are included:

• Introduction
• Preliminary results
• Existence and localization result
• Example

The following sections are included:

• Introduction
• Definitions and preliminary results
• Main result
• Example

Qualitative analysis of differential equations has had an increasingly important role, especially the analytic study of their asymptotic behavior and stability…

The following sections are included:

• Introduction
• Preliminaries
• Existence and localization of homoclinics
• Example of a discontinuous BVP
• Duffing equation
• Forced cantilever beam equation with damping

The following sections are included:

• Introduction
• Definitions and auxiliary results
• Existence results
• Example
• Bernoulli–Euler–v. Karman problem
• Extended Fisher–Kolmogorov and Swift–Hohenberg problems

The following sections are included:

• Introduction
• Auxiliary definitions and Green’s functions
• Existence result
• An infinite beam resting on granular foundations

This part combines several fields of differential and integral equations, such as heteroclinic connections between two equilibrium points, semi-linear problems, or problems with ϕ-Laplacian equations, and integral equations of Hammerstein type, all of them defined on the whole real line…

The following sections are included:

• Introduction
• Definitions and preliminary results
• Existence of heteroclinics
• Example

The following sections are included:

• Introduction
• Auxiliary results
• Existence of heteroclinics solutions
• Example

The following sections are included:

• Introduction
• Existence results
• Example
• Singular ϕ-Laplacian equations

The following sections are included:

• Introduction
• Main result
• Application to fourth-order BVPs and infinite beams

Many phenomena of real life have a retrospective effect, i.e., their status in the future may depend not only on the present but also on what happened in the past. One of the mathematical processes appropriate to study this effect distributed over time is given by Functional Differential Equations (FDEs). It should be noted that the concept of FDEs generalizes the common differential equations into functions with a continuous argument…

The following sections are included:

• Introduction
• Definitions and auxiliary results
• Existence and localization result
• Example
• Emden–Fowler equation

The following sections are included:

• Introduction
• Definitions and a priori bounds
• Existence and localization results
• Falkner–Skan equation

The following sections are included:

• Introduction
• Preliminary results
• Existence and localization result
• Examples

The following sections are included:

• Bibliography
• Index