Variational characterisation of nodal solutions of a Sturm-Liouville problem with strong nonlinearity

Abstract

We consider sublinear Sturm-Liouville problem -u''+ψ(t) |u |p-1 u =λ u, p>1, u(0)=u(1)=0 where ψ is positive and continuous. Using the Nehari variational technique and critical point theory we prove that for each nN there is unique (up to the sign) n-nodal solution of the b.v.p. which is the critical point of a restricted functional associated to the problem