Localization of positive critical points in Banach spaces and applications


Two critical point theorems of M. Schechter in a ball of a Hilbert space are extended to uniformly convex Banach spaces by exploiting the properties of the duality mapping. Moreover, the critical points are sought in the intersection of a ball with a wedge, in particular with a cone, making possible applications to positive solutions of variational problems. The extension from Hilbert to Banach spaces not only requires a major refining of reasoning, but also a different statement by adding a third possibility to the original two alternatives from Schechter’s results. The theory is applied to positive solutions for \(p)\-Laplace equations.


Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

Csaba Varga
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania


Critical point; mountain pass lemma; positive solution; p-Laplace equation

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R. Precup, C. Varga, Localization of positive critical points in Banach spaces and applications, Topol. Methods Nonlinear Anal. 49 (2017), 817-833.


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