Many nonlinear problems in physics, engineering, biology and social sciences can be reduced to finding critical points of functionals. While minimax and Morse theories provide answers to many situations and problems on the existence of multiple critical points of a functional, they often cannot provide much-needed additional properties of these critical points. Sign-changing critical point theory has emerged as a new area of rich research on critical points of a differentiable functional with important applications to nonlinear elliptic PDEs. Key features of this book: (1) Self-contained in-depth treatment of sign-changing critical point theory; (2) Further explorations in Minimax and Morse theories; (3) Topics devoted to linking and nodal solutions, the sign-changing saddle point theory, the generalized Brezis–Nirenberg critical point theorem, the parameter dependence of sign-changing critical points. Expands on a new theorem that has never before been seen in book form Explores applications in each chapter that involve Schrödinger equations or Dirichlet boundary value problems Generalizes the Brezis-Nirenberg critical point theorem Solves a vital open question involving the saddle point theory Obtains the relationship betweenthe classical symmetric mountain pass theorem and the sign-changing critical points INDICE: Preface.- Introduction.- 1. Preliminaries.- 2. Sign-changing critical points via linking.- 3. Sign-changing saddle point.- 4. On a Brezis-Nirenberg theorem.- 5. Even functionals.- 6. Nonsymmetric functionals.- 7. Parameterdependence.- Bibliography.- Index.
- ISBN: 978-0-387-76657-7
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 325
- Fecha Publicación: 01/06/2008
- Nº Volúmenes: 1
- Idioma: Inglés