Singularly perturbed methods for nonlinear elliptic problems
by Cao, Daomin
"The development of variational methods is centered around a fundamental goal, namely, to and solutions for partial differential equations with variational structure. The history of such methods dated back to the 19th century. Despite its long history, these methods still have strong impact in today's research. New critical point theories, such as the mountain pass lemma of Ambrosetti and Rabinowitz, and the concentration compactness principle of P.L.Lions (see also Aubin [10], Brezis and Niren…
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- Full title :Singularly perturbed methods for nonlinear elliptic problems / Daomin Cao, Shuangjie Peng, Shusen Yan.
Summary
"The development of variational methods is centered around a fundamental goal, namely, to and solutions for partial differential equations with variational structure. The history of such methods dated back to the 19th century. Despite its long history, these methods still have strong impact in today's research. New critical point theories, such as the mountain pass lemma of Ambrosetti and Rabinowitz, and the concentration compactness principle of P.L.Lions (see also Aubin [10], Brezis and Nirenberg [24]) have led to many beautiful results on the existence of nontrivial solutions for super-linear elliptic problems. However, these results are not very effective in ending solutions with higher energy for non-compact elliptic problems"--
Read More ↓Edition Statements
- Publication Date:©2021
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge, United Kingdom
- Language:eng
- Publication Date:©2021
The Physical Object
- Description:ix, 252 pages : : illustrations ; : 24 cm.
Edition Identifiers
- ISBN:9781108836838, 1108836836
- oclc:on1182019640
- LC Classification:QA377
- Dewey Decimal:515/.3533
Table of Contents
Machine generated contents note: 1.Non-compact Elliptic Problems -- 1.1.Minimization Problems with Compactness -- 1.2.Non-compact Minimization Problems -- 1.3.Mountain Pass Lemma -- 1.4.Global Compactness -- 1.5.Further Results and Comments -- 2.Perturbation Methods -- 2.1.Locating the Concentration Points -- 2.2.Peak. Solutions for Nonlinear Schrodinger Equations -- 2.3.Existence of Clustering Peak Solutions -- 2.4.Existence of Bubbling Solutions for Problems with Critical Growth -- 2.5.Further Results and Comments -- 3.Local Uniqueness of Solutions -- 3.1.Local Uniqueness of Peak Solutions -- 3.2.Local Uniqueness of Bubbling Solutions -- 3.3.Further Results and Comments -- 4.Construction of Infinitely Many Solutions -- 4.1.The Main Result -- 4.2.Energy Expansion for the Approximate Solutions -- 4.3.The Reduction -- 4.4.The Finite Dimensional Problem -- 4.5.Further Results and Comments -- 5.A Compactness Theorem and Application -- 5.1.The Decomposition -- 5.2.Some Integral Estimates -- 5.3.Estimates on Safe Regions -- 5.4.Proof of the Main Results -- 5.5.Estimates for Linear Problems -- 5.6.Further Results and Comments -- 6.Appendix -- 6.1.Some Elementary Estimates -- 6.2.Pohozae…
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