JournalszaaVol. 20, No. 3pp. 727–737

Quadratic Forms and Nonlinear Non-Resonant Singular Second Order Boundary Value Problems of Limit Circle Type

  • R.P. Agarwal

    National University of Singapore, Singapore
  • Donal O'Regan

    National University of Ireland, Galway, Ireland
  • V. Lakshmikantham

    Florida Institute of Technology, Melbourne, USA
Quadratic Forms and Nonlinear Non-Resonant Singular Second Order Boundary Value Problems of Limit Circle Type cover

Abstract

New existence results are presented for non-resonant second order singular boundary value problems

1p(t)(p(t)y(t))+τ(t)y(t)=λf(t,y(t))  a.e.on  [0,1]\frac {1}{p(t)}(p(t)y'(t))' + \tau (t)y(t) = \lambda f(t,y(t)) \ \ \mathrm {a.e. on \ \ [0,1]}
limt0+p(t)y(t)=y(1)=0\mathrm {lim}_{t\to 0^+} p(t)y'(t) = y (1) = 0

where one of the endpoints is regular and the other may be singular or of limit circle type.

Cite this article

R.P. Agarwal, Donal O'Regan, V. Lakshmikantham, Quadratic Forms and Nonlinear Non-Resonant Singular Second Order Boundary Value Problems of Limit Circle Type. Z. Anal. Anwend. 20 (2001), no. 3, pp. 727–737

DOI 10.4171/ZAA/1041