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A systematic introduction to the singularly perturbed methods in the study of concentration solutions for nonlinear elliptic problems.
List of contents
1. Non-Compact Elliptic Problems; 2. Perturbation Methods; 3. Local Uniqueness of Solutions; 4. Construction of Infinitely Many Solutions; 5. A Compactness Theorem and Application; 6. The Appendix.
About the author
Daomin Cao is a professor at the Institute of Applied Mathematics, Chinese Academy of Sciences. His research focuses on nonlinear partial differential equations. He was awarded the first-class prize of Outstanding Young Scientists of Chinese Academy of Sciences. He is the editor of academic mathematical journals including Applicable Analysis, Annales Academiac Scientiarum Fennicae Mathematica, and Acta Mathematicae Applicatae Sinica.Shuangjie Peng is a professor at the School of Mathematics and Statistics, Central China Normal University. His research focuses on nonlinear elliptic problems. He was awarded the first-class prize of Natural Sciences of Hubei province and the second-class prize of Natural Sciences from the Ministry of Education. He is the editor of academic mathematical journals including Communications on Pure and Applied Analysis, Acta Mathematica Scientia, and Acta Mathematicae Applicatae Sinica.Shusen Yan is a professor at the School of Mathematics and Statistics, Central China Normal University. His main research interests are in nonlinear elliptic problems.
Summary
This book introduces singularly perturbed methods in a self-contained manner by investigating two relatively simple but typical non-compact elliptic problems. Avoiding using too many sophisticated estimates, this book is written for PhD students and junior mathematicians who plan to do their research in the area of elliptic differential equations.
