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

This article is cited in 11 scientific papers (total in 11 papers)

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

Full text: PDF file (257 kB)
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English version:
Mathematical Notes, 2004, 75:2, 259–271

Bibliographic databases:

UDC: 513.88, 517.9
Received: 22.04.2002

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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    Citing articles on Google Scholar: Russian citations, English citations
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    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  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    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  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    3. Kristály A., “Multiple solutions of a sublinear Schrödinger equation”, NoDEA Nonlinear Differential Equations Appl., 14:3-4 (2007), 291–301  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Faraci F., Iannizzotto A., Lisei H., Varga Cs., “A multiplicity result for hemivariational inequalities”, J. Math. Anal. Appl., 330:1 (2007), 683–698  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    5. Yu. V. Malykhin, “Convexity Condition in Cucker–Smale Theorems in the Theory of Teaching”, Math. Notes, 84:1 (2008), 142–146  mathnet  crossref  crossref  mathscinet  isi  elib
    6. Ricceri B., “Minimax theorems for functions involving a real variable and applications”, Fixed Point Theory, 9:1 (2008), 275–291  mathscinet  zmath  isi  elib
    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  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    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  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    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  mathnet  crossref  mathscinet
    10. A. R. Alimov, “On finite-dimensional Banach spaces in which suns are connected”, Eurasian Math. J., 6:4 (2015), 7–18  mathnet
    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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