Minimization on spheres of coercive functionals on View the MathML source

We deal with the minimization on spheres of functionals defined on the space View the MathML sourceW01,2(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[, View the MathML sourceh∈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.