Solutions with multiple alternate sign peaks along a boundary geodesic to a semilinear Dirichlet problem

We study the existence of sign-changing multiple interior spike solutions for the following Dirichlet problem ε^2∆v−v+f(v)=0 in Ω, v=0 on ∂Ω, where Ω is a smooth and bounded domain of R^n, ε is a small positive parameter, f is a superlinear, subcritical and odd nonlinearity. In particular we prove that if Ω has a plane of symmetry and its intersection with the plane is a two-dimensional strictly convex domain, then, provided that k is even and sufficiently large, a k-peak solution exists with alternate sign peaks aligned along a closed curve near a geodesic of ∂Ω.