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A nondifferentiable extension of a theorem of Pucci and Serrin and applications. (English) Zbl 1134.35052

Summary: We study the multiplicity of critical points for functionals which are only differentiable along some directions. We extend to this class of functionals the three critical point theorem of Pucci and Serrin and we apply it to a one-parameter family of functionals \(J_{\lambda }\), \(\lambda \in I \subset \mathbb R\). Under suitable assumptions, we locate an open subinterval of values \(\lambda\) in \(I\) for which \(J_{\lambda }\) possesses at least three critical points. Applications to quasilinear boundary value problems are also given.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35J20 Variational methods for second-order elliptic equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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