Localization Approaches in Strongly Indefinite Problems
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This book discusses some new abstract methods together with their applications to several localization problems, whose common feature is to involve semilinear partial differential equations with a strongly indefinite structure. This book deals with a variety of partial differential equations, including nonlinear Dirac equation from quantum physics (which is of first order), coupled system of multi-component incongruent diffusion and spinorial Yamabe type equations on spin manifolds. The unified framework in this book covers not only the existence of solutions to these PDEs problems, but also asymptotic behaviors of these solutions. In particular, the results for the nonlinear Dirac equations show several concentration behaviors of semiclassical standing waves under the effect of external potentials and the results for the spinorial Yamabe type equations show the existence of conformal embeddings of the 2-sphere into Euclidean 3-space with prescribed mean curvature.
This book will be appealing to a variety of audiences including researchers, postdocs, and advanced graduate students who are interested in strongly indefinite problems.
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Yanheng Ding, Professor of Jilin University and Academy of Mathematics and Systems Science, Chinese Academy of Science. His research interests include nonlinear functional analysis, critical point theory and its applications in PDEs. He received the Alexander von Humboldt research fellowship in 1996.
Tian Xu, Professor of Department of Mathematics, Zhejiang Normal University. His research interests include variational methods for strongly indefinite problems, analytical problems in conformal geometry and its applications. He received the Alexander von Humboldt research fellowship in 2017.
