Vol. 104, No. 1, 1983

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ISSN: 0030-8730
Limit circle type results for sublinear equations

John R. Graef

Vol. 104 (1983), No. 1, 85–94
Abstract

Recently there has been an interest in obtaining integrability criteria for solutions of nonlinear differential equations similar in nature to those known for linear equations. In the classic paper on the subject, H. Weyl classified the second order linear differential equation

(a(t)x′)′+ q(t)x = 0
(1)

as being of the limit circle type if all its solutions are square integrable,i.e.,

∫ ∞
x2(u)du < ∞;

otherwise the equation was said to be of the limit point type. In this paper we discuss extensions of the limit point-limit circle classification to forced second order nonlinear equations of the type

     ′′
(a(t)x) + q(t)f(x) = r(t).
(2)

Mathematical Subject Classification 2000
Primary: 34C11
Secondary: 34B20
Milestones
Received: 29 August 1979
Published: 1 January 1983
Authors
John R. Graef