Solutions of Nonlinear Differential Equations

Existence Results via the Variational Approach

Variational methods are very powerful techniques in nonlinear analysis and are extensively used in many disciplines of pure and applied mathematics (including ordinary and partial differential equations, mathematical physics, gauge theory, and geometrical analysis).

In our first chapter, we gather the basic notions and fundamental theorems that will be applied throughout the chapters. 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 how variational methods can be used in fourth-order problems, Kirchhoff problems, nonlinear field problems, gradient systems, and variable exponent problems. A very extensive bibliography is also included.

Contents:

• Preface
• Some Notations and Conventions
• Preliminaries and Variational Principles
• Quasilinear Fourth-Order Problems
• Kirchhoff Problems
• Nonlinear Field Problems
• Gradient Systems
• Variable Exponent Problems

Readership: Graduate students and researchers interested in variational methods.
Key Features:

• Each section contains supplementary comments and bibliographical notes
• The style and the choice of the material make it accessible to all newcomers to the field
• There is a rich bibliography and an index to aid the reader