Rocky Mountain Journal of Mathematics

Eigenvalue Asymptotics for a Non-Selfadjoint Elliptic Problem Involving an Indefinite Weight

Melvin Faierman

Full-text: Open access

Article information

Rocky Mountain J. Math., Volume 25, Number 1 (1995), 179-187.

First available in Project Euclid: 5 June 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Faierman, Melvin. Eigenvalue Asymptotics for a Non-Selfadjoint Elliptic Problem Involving an Indefinite Weight. Rocky Mountain J. Math. 25 (1995), no. 1, 179--187. doi:10.1216/rmjm/1181072276.

Export citation


  • S. Agmon, On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems, Comm. Pure Appl. Math. 15 (1962), 119-147.
  • --------, Lectures on elliptic boundary value problems, Van Nostrand, Princeton, NJ, 1965.
  • --------, On kernels, eigenvalues, and eigenfunctions of operators related to elliptic problems, Comm. Pure Appl. Math. 18 (1965), 627-663.
  • M.S. Birman and M.Z. Solomjak, Spectral asymptotics of nonsmooth elliptic operators II, Trans. Moscow Math. Soc. 28 (1973), 1-32.
  • --------, Asymptotic behaviour of the spectrum of differential equations, J. Soviet Math. 12 (1974), 247-282.
  • --------, Asymptotics of the spectrum of variational problems on solutions of elliptic equations, Siberian Math. J. 20 (1979), 1-15.
  • --------, Quantitative analysis in Sobolev imbedding theorems and applications to spectral theory, Amer. Math. Soc. Transl. 114 (1980).
  • M. Faierman, On the eigenvalues of nonselfadjoint problems involving indefinite weights, Math. Ann. 282 (1988), 369-377.
  • --------, Non-selfadjoint elliptic problems involving an indefinite weight, Comm. Partial Differential Equations 15 (1990), 939-982.
  • J. Fleckinger and M.L. Lapidus, Eigenvalues of elliptic boundary value problems with an indefinite weight function, Trans. Amer. Math. Soc. 295 (1986), 305-324.
  • --------, Remainder estimates for the asymptotics of elliptic eigenvalue problems with indefinite weights, Arch. Rational Mech. Anal. 98 (1987), 329-356.
  • I.C. Gohberg and M.G. Krein, Introduction to the theory of linear nonselfadjoint operators, Amer. Math. Soc., Providence, 1969.
  • P. Hess, On the asymptotic distribution of eigenvalues of some nonselfadjoint problems, Bull. London Math. Soc. 18 (1986), 181-184.
  • --------, On the spectrum of elliptic operators with respect to indefinite weights, Linear Algebra Appl. 84 (1986), 99-109.
  • T. Kato, Perturbation theory for linear operators, 2nd ed., Springer-Verlag, New York, 1976.
  • J.L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications, Vol. I, Springer-Verlag, New York,
  • 1972. M. Schechter, General boundary value problems for elliptic partial differential equations, Comm. Pure Appl. Math. 12 (1959), 457-482.