Higher Order Boundary Value Problems on Unbounded Domains

Types of Solutions, Functional Problems and Applications

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.

Contents:

• Boundary Value Problems on the Half-Line:

  • Third-Order Boundary Value Problems
  • General nth-Order Problems
  • Impulsive Problems on the Half-Line with Infinite Impulse Moments

• Homoclinic Solutions and Lidstone Problems:

  • Homoclinic Solutions for Second-Order Problems
  • Homoclinic Solutions to Fourth-Order Problems
  • Lidstone Boundary Value Problems

• Heteroclinic Solutions and Hammerstein Equations:

  • Heteroclinic Solutions for Semi-Linear Problems (i)
  • Heteroclinic Solutions for Semi-Linear Problems (ii)
  • Heteroclinic Solutions for Semi-Linear Problems (iii)
  • Hammerstein Integral Equations with Sign-Changing Kernels

• Functional Boundary Value Problems:

  • Second-Order Functional Problems
  • Third-Order Functional Problems
  • ϕ-Laplacian Equations with Functional Boundary Conditions

Readership: Graduate students and researchers interested in nonlinear analysis.
Key Features:

• Presents higher order boundary value and impulsive problems on unbounded domains
• Elucidates homoclinic and heteroclinic solutions without growth, sign or periodicity assumptions on the nonlinearity, and their relation with Lidstone problems and Hammerstein equations on the real line
• Explains clearly the semi-linear and higher order functional problems where the boundary conditions can include nonlocal data and global variation on the unknown functions, such as multi-point, integral, maximum and/or minimum arguments