Multiple Solutions of Boundary Value Problems

A Variational Approach

Variational methods and their generalizations have been verified to be useful tools in proving the existence of solutions to a variety of boundary value problems for ordinary, impulsive, and partial differential equations as well as for difference equations. In this monograph, we look at how variational methods can be used in all these settings. In our first chapter, we gather the basic notions and fundamental theorems that will be applied in the remainder of this monograph. While many of these items are easily available in the literature, we gather them here both for the convenience of the reader and for the purpose of making this volume somewhat self-contained. Subsequent chapters deal with the Sturm–Liouville problems, multi-point boundary value problems, problems with impulses, partial differential equations, and difference equations. An extensive bibliography is also included.

Contents:

• Mathematical Preliminaries
• Sturm–Liouville Problems
• Multi-Point Problems
• Impulsive Problems
• Partial Differential Equations
• Difference Equations

Readership: Graduate students and researchers interested in applying variational methods to a variety of boundary value problems.
Key Features:

• Currently, no other book focuses on applying variational methods to solving various types of boundary value problems
• The basic tools needed to explore these kinds of problems are gathered into one place
• Includes an extensive bibliography