Fixed point–critical point hybrid theorems and application to systems with partial variational structure


In this paper, fixed point arguments and a critical point technique are combined leading to hybrid existence results for a system of two operator equations where only one of the equations has a variational structure. An application to periodic solutions of a semi-variational system is given to illustrate the theory.


Irene Benedetti
University of Perugia, Italy

Tiziana Cardinali
University of Perugia, Italy

Radu Precup
Babeş-Bolyai University, Romania


Ekeland variational principle; Krasnosel’skii’s fixed point theorem for the sum of two operators; Perov contraction; Positive solution; Periodic problem; Second-order differential systems



Cite this paper as:

I. Benedetti, T. Cardinali, R. Precup, Fixed point–critical point hybrid theorems and application to systems with partial variational structure, Journal of Fixed Point Theory and Applications volume 23, Article number: 63 (2021),

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