Singularly Perturbed Methods for Nonlinear Elliptic Problems

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.

• 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.

'This book presents in a very nice and self-contained manner the main methods to find (or to construct) solutions, which exhibit a concentration property, to non-compact elliptic problems.' Lutz Recke, ZB Math Reviews