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 [Formula: see text] where Ω is a smooth and bounded domain of ℝN, 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.