Multiplicity results for some elliptic problems with concave nonlinearities (Q1370989)

An abstract linking theorem, which concludes the existence of a pair of critical points, is established. In contrast with the result of \textit{M. Schechter} [Appl. Anal. 49, No. 1-2, 33-48 (1993; Zbl 0802.35049)], the author shows that some critical groups are nontrivial in addition. This theorem is applied to study multiple solutions for the asymptotically linear elliptic boundary value problem with a perturbation term \(\lambda|u|^{q-2}u\), \(1<q<2\), and \(\lambda>0\) small.