Spike layered solutions ( solutions concentrating in zero dimensional sets ) in bounded domain Ω with Dirichlet and Neumann boundary condition have been studied in recent years by many authors

In this paper we construct a new kind of positive solutions of ∆u− u + u = 0 on R when p > 2. These solutions have the following asymptotic behavior u(x, z) ∼ ω(x− f(z)) + ∞ ∑ i=1 ω0((x, z)− ξi~e1) as L → +∞ where ω is a unique positive homoclinic solution of ω′′−ω+ωp = 0 in R ; ω0 is the two dimensional positive solution and ~e1 = (1, 0) and ξj are points… CONTINUE READING