Multi-bump solutions for nonlinear elliptic equations involving critical Sobolev exponents
- Authors
- Jin, S.
- Issue Date
- Jul-2022
- Publisher
- Elsevier Ltd
- Keywords
- Critical problem; Expanding domain; Multi-bump solutions
- Citation
- Nonlinear Analysis, Theory, Methods and Applications, v.220
- Journal Title
- Nonlinear Analysis, Theory, Methods and Applications
- Volume
- 220
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/61277
- DOI
- 10.1016/j.na.2022.112829
- ISSN
- 0362-546X
1873-5215
- Abstract
- We study the existence of multi-bump solutions of −Δu−λu=up,u>0inΩt,u=0on∂Ωt,where λ is a real constant, N≥3, [Formula presented], and Ωt is a domain that expands as t→∞. It is known that the topology of the domain Ωt affects the existence and non-existence of solutions. In this article, we prove the existence of multi-bump solutions for more general domains; for example, Ωtball≡{tq+v|q∈M,v∈(TqM)⊥,|v|<1} or Ωtann={tq+v|q∈M,v∈(TqM)⊥,a<|v|<a+1}, where a>0 and M is a k-dimensional compact smooth submanifold of RN without boundary (k=1,⋯,N−1). © 2022 Elsevier Ltd
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