Multiplicity theorems involving functions with non-convex range

Authors

  • Biagio RICCERI University of Catania, Italy e-mail: ricceri@dmi.unict.it

DOI:

https://doi.org/10.24193/subbmath.2023.1.09

Keywords:

Minimax, global minimum, multiplicity, non-convex sets, Chebyshev sets, Kirchhoff-type problems.

Abstract

Here is a sample of the results proved in this paper.

Mathematics Subject Classification (2010): 49J35, 34B10, 41A50, 41A55, 90C26.

Received 03 May 2022; Revised 09 September 2022. Published Online: 2023-03-20. Published Print: 2023-04-30

Author Biography

Biagio RICCERI, University of Catania, Italy e-mail: ricceri@dmi.unict.it

Department of Mathematics and Informatics, University of Catania, Viale A. Doria 6, 95125 Catania, Italy e-mail: ricceri@dmi.unict.it

References

Alimov, A.R., Tsar’kov, I.G., Connectedness and solarity in problems of best and near-best approximation, Russian Math. Surveys, 71(2016), 1-77.

Balagansk˘ıi, V.S., Vlasov, L.P., The problem of the convexity of Chebyshev sets, Russian Math. Surveys, 51(1996), 1127-1190.

Efimov, N.V., Ste˘ckin, S.B., Approximative compactness and Chebyshev sets, Dokl. Akad. Nauk SSSR, 140(1961), 522-524.

Faraci, F., Iannizzotto, A., An extension of a multiplicity theorem by Ricceri with an application to a class of quasilinear equations, Studia Math., 172(2006), 275-287.

Faraci, F., Iannizzotto, A., Well posed optimization problems and nonconvex Chebyshev sets in Hilbert spaces, SIAM J. Optim., 19(2008), 211-216.

Pucci, P., Serrin, J., A mountain pass theorem, J. Differential Equations, 60(1985), 142-149.

Ricceri, B., A general multiplicity theorem for certain nonlinear equations in Hilbert spaces, Proc. Amer. Math. Soc., 133(2005), 3255-3261.

Ricceri, B., A conjecture implying the existence of non-convex Chebyshev sets in infinite-dimensional Hilbert spaces, Matematiche, 65(2010), 193-199.

Ricceri, B., On a minimax theorem: an improvement, a new proof and an overview of its applications, Minimax Theory Appl., 2(2017), 99-152.

Tsar’kov, I.G., Nonuniqueness of solutions of some differential equations and their connection with geometric approximation theory, Math. Notes, 75(2004), 259-271.

Zeidler, E., Nonlinear Functional Analysis and its Applications, vol. III, Springer-Verlag, 1985.

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Published

2023-03-20

How to Cite

RICCERI, B. (2023). Multiplicity theorems involving functions with non-convex range. Studia Universitatis Babeș-Bolyai Mathematica, 68(1), 125–137. https://doi.org/10.24193/subbmath.2023.1.09

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