Skip to main content
SpringerLink
Log in

On the bilaplacian problem with nonlinear boundary conditions

  • Published:
Indian Journal of Pure and Applied Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we present a study for a nonlinear problem governed by the biharmonic equation in the plane. Using Green’s formula, the problem is converted into a system of nonlinear integral equations for the unknown data of the boundary. Existence and uniqueness of the solution of the system of nonlinear boundary integral equations is established.

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. K. Aziz and I. Babuska, Mathematical foundation of the finite element method with applications to partial differential equation, Academic press, New York (1972).

    Google Scholar 

  2. F. E. Browder, Nonlinear elliptic boundary value problems, I. Bull. Am. Math. Soc., 69 (1963), 862–875.

    Article  MathSciNet  MATH  Google Scholar 

  3. C. A. Brebbia, J. C. F. Telles and L. C. Wrobel, Boundary Element Techniques, Springer, Verlag, Berlin (1984).

    Book  MATH  Google Scholar 

  4. J. Kohn and L. Nirenberg, On the algebra of pseudo différential operators, Comm. Pure Appl. Math., 18 (1968).

  5. G. Hsiao and W. L.Wendland, Boundary integral equations, App. Math. Sciences, Springer, 164 (2008).

    Google Scholar 

  6. G. Minty, Monotone operators in Hilbert spaces, Duke Math. J., 29 (1962), 341–346.

    Article  MathSciNet  MATH  Google Scholar 

  7. H. Saker, On the Harmonic problem with boundary integral conditions, International Journal of Analysis, (2014), ID 976520.

    Google Scholar 

  8. K. Ruotsalainen and W. Wendland, On the boundary element method for some nonlinear boundary value problems, Numerische. Mathematik, 53 (1988), 299–314.

    Article  MathSciNet  MATH  Google Scholar 

  9. F. Cakoni, G. C. Hsiao and W. Wendland, On the boundary integral equation method for a mixed boundary value problem of the biharmonic equation, Complex Variables, 50 (2005) 681–696.

    Article  MathSciNet  MATH  Google Scholar 

  10. F. Treves, Introduction to pseudodifferential and fourier integral operators, Plenum press, New York (1980).

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. L.M.A. Department of Mathematics, Faculty of Sciences, University of Badji Mokhtar, P. O. Box 12, Annaba, 23000, Algeria

    Hacene Saker & Naila Bouselsal

Authors
  1. Hacene Saker
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Naila Bouselsal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hacene Saker.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Saker, H., Bouselsal, N. On the bilaplacian problem with nonlinear boundary conditions. Indian J Pure Appl Math 47, 425–435 (2016). https://doi.org/10.1007/s13226-016-0178-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13226-016-0178-3

Key words

Search

Navigation