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In this paper, we deal with equations of variational form which Naharimanifolds can contain more than two different types of critical points. Weintroduce a method of separating critical points on the Nahari manifold, basedon the use of nonlinear generalized Rayleigh quotients. The method isillustrated by establishing the existence of positive solutions, ground statesand multiplicity results for a two-parameter nonlinear elliptic boundaryproblem with polynomial nonlinearities.

Separating of critical points on the Nehari manifold via the nonlinear generalized Rayleigh quotients