A critical point theorem with a relaxed boundary condition and critical groups (Q1968654)

A critical point theorem with an information on the Morse critical groups has been proved by the author in [J. Differ. Equations 140, No. 1, 142-160 (1997; Zbl 0889.58025)]. In the present paper the author extends this result to the case of the so-called relaxed boundary conditions in the spirit of \textit{N. Ghoussoub} [Proc. Am. Math. Soc. 117, No. 2, 439-447 (1993; Zbl 0791.49028)]. As an application a new multiplicity result for a superlinear Sturm-Liouville equation under Neumann boundary condition is given. Information on the critical groups from the abstract theorem is used to distinguish between constant and nonconstant solutions.