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Positive Solutions of the Equation U + U P = 0 on a Bounded Domain
| Content Provider | Semantic Scholar |
|---|---|
| Author | Vorst, Robertus Van Der |
| Copyright Year | 2007 |
| Abstract | These are are the notes of a series of lectures given in the seminar "Topics in Nonlinear Analysis" at the "Center for Nonlinear Partial Diierential Equations (Delft-Leiden)", in autumn of 1991. In these course notes we present the basic theorems, and the necessary background as a selfcontained resum e on the problem (P) n u + u p = 0 in ; u = 0 on @: We restrict ourselves mainly to the subcritical case (1 < p < (n + 2)=(n ? 2)), and we only consider positive solutions. Our choice of topics is largely determined by one of the goals of the seminar, which is to present recent results in a self-contained form, with details lled in as much as possible. We chose to do S.C. Lin's recent uniqueness theorem for positive solutions of (P) with Morse index 1 on convex domains in dimension 2 L]. Thus, besides a careful proof of the standard existence results in terms of weak solutions and mountain passes, we also treat applications of the implicit function theorem, which require knowledge of the linearized problem. Moreover we discuss the nature of the numerous integral identities that have been around (see e.g. P,PS,vdV1]) for solutions of (P) and related problems. This goes back to E. Noether N]. We would like to thank Fred Weissler for a number of fruitful discussions, and Franc e Ouwerkerk-Persaud for typing the handwritten notes. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.math.leidenuniv.nl/~hulshof/21.ps |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
