In a recent paper, H. Amann and E. Zehnder [ 11 studied existence problems for equations of the form (1) in a real Hilbert space H. Here A is a selfadjoint linear operator and F is a potential operator, mapping H continuously into itself. It is well known that equation ( 1) is a good framework for
✦ LIBER ✦
Nontrivial Solutions of Quasilinear Equations via Nonsmooth Morse Theory
✍ Scribed by Jean-Noël Corvellec; Marco Degiovanni
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 417 KB
- Volume
- 136
- Category
- Article
- ISSN
- 0022-0396
No coin nor oath required. For personal study only.
✦ Synopsis
then (P 0 ) has a nontrivial solution.
The same result was then obtained by Chang [8], using Morse theory on manifolds with boundary, and Lazer and Solimini [16], by a combination of min max techniques and classical Morse theory. For some article no. DE963254
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## Paper 1. Introduction We are concerned with the following p.x/-Kirchhoff type equation where R N is a bounded smooth domain, p 2 C with 1 < p .x/ < N. We assume that M and f satisfy the following conditions: .M 1 / M : R C ! R C is a continuous function and satisfies the (polynomial growth) c