✦ LIBER ✦
Critical Points of a Singular Perturbation Problem via Reduced Energy and Local Linking
✍ Scribed by Nicholas Alikakos; Michał Kowalczyk
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 208 KB
- Volume
- 159
- Category
- Article
- ISSN
- 0022-0396
No coin nor oath required. For personal study only.
✦ Synopsis
In this paper we study the existence of critical points of the functional
where 0 # R d , d 2 is a bounded domain with C 3 boundary, u # H 1 (0), and = is a small parameter. On the nonlinearity F we assume:
). Additionally we require that there exists q>1 such that for u>0 the function F$(u)Âu q is nondecreasing and that there exists % # (0, 1Â2) such that %F $(u) u&F(u)>0, u 0. A typical example is F(u)=u 3 Â3, u>0. We point out here that our results apply to a larger class of nonlinearities (see Sect. 3.1 for more details). In the sequel we shall denote F $ by f.