Skip to main content
SpringerLink
Log in

On the solvability of some nonlinear Elliptic problems

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

The solvability of second-order nonlinear elliptic equations in weighted Sobolev spaces is analyzed. An additional condition ensuring the solvability of such equations is that the average of the desired solution over some circle of fixed radius is zero. Examples are equations containing a weighted p-Laplacian and the Euler equations.

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. A. Kufner and S. Fucik, Nonlinear Differential Equations (Elsevier, Amsterdam 1980; Nauka, Moscow, 1988).

    MATH  Google Scholar 

  2. A. Kh. Khanmamedov, “Existence of a global attractor for the parabolic equation with nonlinear Laplacian principal part in an unbounded domain,” J. Math. Anal. Appl. 316 (2), 601–615 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  3. I. Kuzin and S. Pohozaev, Entire Solutions of Semilinear Elliptic Equations, Progress in Nonlinear Differential Equations and Their Applications, Vol. 33 (Birkhäuser, Basel, 1997).

    MATH  Google Scholar 

  4. P. Pucci and R. Servadei, “On weak solutions for p-Laplacian equations with weights,” Discrete Continuous Dyn. Syst., Suppl. Vol., 1–10 (2007).

  5. J. Goncalves and C. Santos, “Positive solutions of a class of quasilinear singular equations,” J. Differ. Equations 56, 1–15 (2004).

    Google Scholar 

  6. A. Khalil, S. Manouni, and M. Ouanan, “On some nonlinear problems for p-Laplacian in Rn,” Nonlinear Differ. Equations Appl. 15, 295–307 (2008).

    Article  MATH  Google Scholar 

  7. Liu Shibo, “On ground states of superlinear p-Laplacian equations in Rn,” J. Math. Anal. Appl. 361, 48–58 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  8. Yu. A. Dubinskii, “Hardy inequalities with exceptional parameter values and applications,” Dokl. Math. 80 (1), 558–562 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  9. Yu. A. Dubinskii, “On a scale of Hardy-type integral inequalities,” Dokl. Math. 81 (1), 111–114 (2010).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Research University “MPEI,”, Moscow, 111250, Russia

    E. V. Golubeva & Yu. A. Dubinskii

Authors
  1. E. V. Golubeva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. A. Dubinskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. V. Golubeva.

Additional information

Original Russian Text © E.V. Golubeva, Yu.A. Dubinskii, 2017, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 3, pp. 404–416.

In memory of S.I. Pohozaev

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Golubeva, E.V., Dubinskii, Y.A. On the solvability of some nonlinear Elliptic problems. Comput. Math. and Math. Phys. 57, 409–421 (2017). https://doi.org/10.1134/S0965542517030058

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542517030058

Keywords

Search

Navigation