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 Mat. Zametki, 2004, Volume 75, Issue 2, Pages 287–301 (Mi mz34)

Nonunique Solvability of Certain Differential Equations and Their Connection with Geometric Approximation Theory

I. G. Tsar'kov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: In this paper, we study the structural and approximative properties of sets admitting an upper semicontinuous acyclic selection from an almost-best approximation operator. We study the questions of nonunique solvability of a nonlinear inhomogeneous Dirichlet problem on the basis of these properties.

DOI: https://doi.org/10.4213/mzm34

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English version:
Mathematical Notes, 2004, 75:2, 259–271

Bibliographic databases:

UDC: 513.88, 517.9

Citation: I. G. Tsar'kov, “Nonunique Solvability of Certain Differential Equations and Their Connection with Geometric Approximation Theory”, Mat. Zametki, 75:2 (2004), 287–301; Math. Notes, 75:2 (2004), 259–271

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz34
• https://doi.org/10.4213/mzm34
• http://mi.mathnet.ru/eng/mz/v75/i2/p287

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Ricceri B., “A general multiplicity theorem for certain nonlinear equations in Hilbert spaces”, Proc. Amer. Math. Soc., 133:11 (2005), 3255–3261
2. Faraci F., Iannizzotto A., “An extension of a multiplicity theorem by Ricceri with an application to a class of quasilinear equations”, Studia Math., 172:3 (2006), 275–287
3. Kristály A., “Multiple solutions of a sublinear Schrödinger equation”, NoDEA Nonlinear Differential Equations Appl., 14:3-4 (2007), 291–301
4. Faraci F., Iannizzotto A., Lisei H., Varga Cs., “A multiplicity result for hemivariational inequalities”, J. Math. Anal. Appl., 330:1 (2007), 683–698
5. Yu. V. Malykhin, “Convexity Condition in Cucker–Smale Theorems in the Theory of Teaching”, Math. Notes, 84:1 (2008), 142–146
6. Ricceri B., “Minimax theorems for functions involving a real variable and applications”, Fixed Point Theory, 9:1 (2008), 275–291
7. Breckner B. E., Varga Cs., “A multiplicity result for gradient-type systems with non-differentiable term”, Acta Math. Hungar., 118:1-2 (2008), 85–104
8. Breckner B. E., Horváth A., Varga C., “A multiplicity result for a special class of gradient-type systems with non-differentiable term”, Nonlinear Anal., 70:2 (2009), 606–620
9. A. R. Alimov, I. G. Tsar'kov, “Connectedness and other geometric properties of suns and Chebyshev sets”, J. Math. Sci., 217:6 (2016), 683–730
10. A. R. Alimov, “On finite-dimensional Banach spaces in which suns are connected”, Eurasian Math. J., 6:4 (2015), 7–18
11. A. R. Alimov, I. G. Tsar'kov, “Connectedness and solarity in problems of best and near-best approximation”, Russian Math. Surveys, 71:1 (2016), 1–77
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