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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Ekeland's Variational Principle for Functions Unbounded from below

Discontinuity, Nonlinearity, and Complexity 9(4) (2020) 553--558 | DOI:10.5890/DNC.2020.12.008

R. Sengupta$^{1}$ , S. Zhukovskiy$^{2}$

$^1$ Faculty of Science, Peoples' Friendship University of Russia, 117198, Moscow, Mikluho-Maklaya st., 6

$^2$ V. A. Trapeznikov Institute of Control Sciences of RAS,117997, Moscow, Profsoyuznaya st., 65

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A modification of the Ekeland variational principle for functions unbounded from below is obtained. For a wide class of differentiable functions not necessarily bounded below, it is shown that there exists a minimizing sequence satisfying the first-order necessary conditions, up to any desired approximation.


The research is supported by the Volkswagen Foundation and the Russian Foundation for Basic Research (Projects No 20-31-70013, 19-01-00080). The results in Section 3 are due to the second author who was supported by the Russian Science Foundation (Project No 20-11-20131).


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