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Some remarks on a three critical points theorem. (English) Zbl 1031.49006
This paper establishes several applications to nonlinear boundary value problems of the three critical points theorem of Ricceri. First, the author proves several abstract results related to a strict minimax inequality. As applications, there are established multiplicity results for nonlinear elliptic problems, including: (i) a two-point boundary value problem, (ii) a Dirichlet problem for semilinear elliptic equations with discontinuous nonlinearities, and (iii) a nonlinear Neumann boundary problem. The proofs rely on refined arguments in the critical point theory.

49J35Minimax problems (existence)
35B38Critical points in solutions of PDE
34B15Nonlinear boundary value problems for ODE
35J65Nonlinear boundary value problems for linear elliptic equations
35R05PDEs with discontinuous coefficients or data
58E05Abstract critical point theory