Skip to main content
Multiple Solutions for an Elliptic Problem Related to Vortex Pairs
Journal of Differential Equations (2011)
  • Yi Li, Wright State University - Main Campus
  • Shuangjie Peng

Let Ω be a bounded domain in RN (N⩾2), φ a harmonic function in Ω¯. In this paper we study the existence of solutions to the following problem arising in the study of vortex pairs(Pλ){−Δu=λ(u−φ)+p−1,x∈Ω,u=0,x∈∂Ω. The set Ωp={x∈Ω,u(x)>φ} is called “vortex core”. Existence of solutions whose “vortex core” consists of one component and asymptotic behavior of “vortex core” were studied by many authors for large λ recently. Under the condition that φ has k strictly local minimum points on the boundary ∂Ω, we obtain in this paper that for λ large enough, (Pλ) has a solution with “vortex core” consisting of k components by a constructive way.

Publication Date
April 15, 2011
Publisher Statement
The downloadable file associated with this record is the authors' preprint.
Citation Information
Yi Li and Shuangjie Peng. "Multiple Solutions for an Elliptic Problem Related to Vortex Pairs" Journal of Differential Equations Vol. 250 Iss. 8 (2011)
Available at: