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Zeitschrift für Analysis und ihre Anwendungen


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Volume 20, Issue 3, 2001, pp. 727–737
DOI: 10.4171/ZAA/1041

Published online: 2001-09-30

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

R.P. Agarwal[1], Donal O'Regan[2] and V. Lakshmikantham[3]

(1) National University of Singapore, Singapore
(2) National University of Ireland, Galway, Ireland
(3) Florida Institute of Technology, Melbourne, USA

New existence results are presented for non-resonant second order singular boundary value problems $$\frac {1}{p(t)}(p(t)y'(t))' + \tau (t)y(t) = \lambda f(t,y(t)) \ \ \mathrm {a.e. on \ \ [0,1]}$$ $$\mathrm {lim}_{t\to 0^+} p(t)y'(t) = y (1) = 0$$ where one of the endpoints is regular and the other may be singular or of limit circle type.

Keywords: Singular and non-resonant problems, points of limit circle type, existence criteria for solutions

Agarwal R.P., O'Regan Donal, Lakshmikantham V.: Quadratic Forms and Nonlinear Non-Resonant Singular Second Order Boundary Value Problems of Limit Circle Type. Z. Anal. Anwend. 20 (2001), 727-737. doi: 10.4171/ZAA/1041