where Ω=Ω1×Ω2⊂ℝN is a bounded domain having cylindrical symmetry, Ω1⊂ℝm is a bounded regular domain and Ω2 is a k-dimensional ball of radius R, centered in the origin and m+k=N, m≧1, k≧2. Under some suitable conditions on the functions a and h, using variational methods we prove that the problem has at least one resp. at least two solutions in two cases: g=0 and g≠0.
 Ambrosetti, A.Rabinowitz, P. H.1973Dual variational methods in critical points theory and applicationsJ. Funct. Anal.4349–381.
Castro, A.Clapp, M.2003The effect of the domain topology on the number of minimal nodal solutions of an elliptic equation at critical growth in a symmetric domainNonlinearity16579–59010.1088/0951-7715/16/2/313.)| false