Minimization on spheres of coercive functionals on W01,2(Ω)

We deal with the minimization on spheres of functionals defined on the space W01,2(Ω). We apply the main results to establish a multiplicity theorem for a Dirichlet problem involving equations of the type −Δu=h(x)|u|s−2u+λg(x,u)−Δu=h(x)|u|s−2u+λg(x,u). Here ΔΔ is the Laplacian operator, λλ is a real parameter, s∈]1,2[s∈]1,2[, h∈C(Ω¯) is a function which is allowed to be sign-changing and g:Ω×R→Rg:Ω×R→R, Ω⊂RNΩ⊂RN is a Carathéodory function having no growth conditions with respect to the second variable.