Let Omega be a bounded domain in R(N) (N >= 2), phi a harmonic function in (Omega) over bar. In this paper we study the existence of solutions to the following problem arising in the study of vortex pairs (P(lambda)) {-Delta u =lambda(u - phi)(+)(p-1), x is an element of Omega, u = 0, x is an element of partial derivative Omega. The set Omega(p) = {x is an element of Omega, u(x) > phi}phi 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 lambda recently. Under the conditi...
