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. Parameter dependence.- Bibliography.- Index.
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.
This book is intended for advanced graduate students and researchers involved in sign-changing critical point theory, PDEs, global analysis, and nonlinear functional analysis.