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3 results

  • Multiparameter Variational Eigenvalue Problems With Indefinite Nonlinearity

  • Tetsutaro Shibata
  • Journal:
    Canadian Journal of Mathematics / Volume 49 / Issue 5 / 01 October 1997
    Published online by Cambridge University Press:
    20 November 2018, pp. 1066-1088
    Print publication:
    01 October 1997
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  • We consider the multiparameter nonlinear Sturm-Liouville problem

    where are parameters. We assume that

    1 ≤ q ≤ p1 < p2 < ... ≤ pn < 2q + 3.

    We shall establish an asymptotic formula of variational eigenvalue λ = λ(μ, α) obtained by using Ljusternik-Schnirelman theory on general level set Nμ, α(α < 0 : parameter of level set). Furthermore,we shall give the optimal condition of {(μ, α)}, under which μi(m + 1 ≤ i ≤ n : fixed) dominates the asymptotic behavior of λ(μ, α).

  • A Comparison of Eigenvalues of Two Sturm-Liouville Problems

  • Yisong Yang
  • Journal:
    Canadian Mathematical Bulletin / Volume 33 / Issue 4 / 01 December 1990
    Published online by Cambridge University Press:
    20 November 2018, pp. 386-390
    Print publication:
    01 December 1990
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  • We compare, under some assumptions on mass density, the eigenvalues of the Sturm-Liouville problems satisfying homogeneous Dirichlet and Neumann boundary condition.

  • Semibounded Extensions of Singular Ordinary Differential Operators

  • Allan M. Krall
  • Journal:
    Canadian Mathematical Bulletin / Volume 31 / Issue 4 / 01 December 1988
    Published online by Cambridge University Press:
    20 November 2018, pp. 432-438
    Print publication:
    01 December 1988
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  • The self-adjoint extensions of the singular differential operator Ly = [(py’)’ + qy]/w, where p < 0, w > 0, q ≧ mw, are characterized under limit-circle conditions. It is shown that as long as the coefficients of certain boundary conditions define points which lie between two lines, the extension they help define has the same lower bound.