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SUPERCRITICAL PROBLEMS IN DOMAINS WITH THIN TOROIDAL HOLESopen access
- Authors
- Kim, Seunghyeok; Pistoia, Angela
- Issue Date
- Nov-2014
- Publisher
- Dept. of Mathematics, Southwest Missouri State University
- Keywords
- Concentration on ℓ-dimensional manifolds; Supercritical problem
- Citation
- Discrete and Continuous Dynamical Systems, v.34, no.11, pp.4671 - 4688
- Indexed
- SCIE
SCOPUS
- Journal Title
- Discrete and Continuous Dynamical Systems
- Volume
- 34
- Number
- 11
- Start Page
- 4671
- End Page
- 4688
- ISSN
- 1078-0947
- Abstract
- In this paper we study the Lane-Emden-Fowler equation (P)ε, ∫, Δu+|q|q-2 u=0 in Dε, u=0 on ∂Dε Here Dε = D\-x ε D : dist(x, λℓ') ≤ ε}, D is a smooth bounded domain in ℝN, λ ℓ in an ℓ- dimensional closed manifold such that λ ℓ ⊂ D with 1 ≤ ℓ ℓ N - 3 and q = 2(N-ℓ)/N-ℓ-2: We prove that, under some symmetry assumptions, the number of sign changing solutions to (P)ε increases as ε goes to zero.
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Related Researcher
- Kim, Seung hyeok
- COLLEGE OF NATURAL SCIENCES (DEPARTMENT OF MATHEMATICS)