Skip to main content
SpringerLink
Log in

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

  • Published:
Mathematical Notes Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. N. Steenrod and S. Eilenberg, Foundations of Algebraic Topology, Princeton University Press, Princeton, New Jersey, 1952.

    Google Scholar 

  2. M. A. Krasnoselľskii and Ya. B. Rutitskii, Convex Functions and Orlicz Spaces [in Russian], Moscow, 1958.

  3. N. Levinson, “Positive eigenfunctions for Δu + λf(u) = 0,” Arch. Rat. Mech. and Analysis, 11 (1962), no. 3, 258–272.

    Google Scholar 

  4. M. A. Krasnoselľskii and V. Ya. Stetsenko, “On nonlinear problems having many solutions” Sibirsk. Mat. Zh. [Siberian Math. J.], 4 (1963), no. 1, 120–137.

    Google Scholar 

  5. S. I. Pokhozhaev, “On the eigenfunctions of the equation Δu + λf(u) = 0,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 165 (1965), no. 1, 36–39.

    Google Scholar 

  6. S. I. Pokhozhaev, “On an approach to nonlinear equations,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 247 (1979), no. 6, 1327–1331.

    Google Scholar 

  7. T. G. Begle, “The Vietoris mapping theorem for bicompact spaces,” Ann. of Math., 51 (1950), no. 3, 534–543.

    Google Scholar 

  8. K. Borsuk, Theory of Retracts, PWN, Warsaw, 1967; Russian translation, Mir, Moscow, 1971.

    Google Scholar 

  9. I. G. Tsarľkov, “On the connectedness of some classes of sets in Banach spaces,” Mat. Zametki [Math. Notes], 40 (1986), no. 2, 174–196.

    Google Scholar 

  10. I. G. Tsarľkov, “Properties of sets possessing continuous selections from the operator P δ” Mat. Zametki [Math. Notes], 48 (1990), no. 4, 122–131.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, Russia

    I. G. Tsar'kov

Authors
  1. I. G. Tsar'kov
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tsar'kov, I.G. Nonunique Solvability of Certain Differential Equations and Their Connection with Geometric Approximation Theory. Mathematical Notes 75, 259–271 (2004). https://doi.org/10.1023/B:MATN.0000015042.89501.ed

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:MATN.0000015042.89501.ed

Search

Navigation