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Zbl 0535.34024
Graef, John R.
Limit circle type results for sublinear equations.
(English)
[J] Pac. J. Math. 104, 85-94 (1983). ISSN 0030-8730

The author considers forced second order nonlinear equations of the type $(a(t)x')'+q(t)f(x)=r(t)$ and calls them of nonlinear limit circle type if every solution x(t) has $\int\sp{\infty}\sb{t\sb 0}x(u)f(x(u))du<\infty$ and of nonlinear limit point type otherwise (this definition generalizes {\it H. Weyl}'s [Math. Ann. 68, 220-269 (1910)] classification of second order linear differential equations $(a(t)x')'+q(t)x=0)$. The author considers the sublinear case $f(x)=x\sp{\gamma}$, $0<\gamma \le 1$. Necessary and sufficient conditions are found that such a forced or unforced $(r=0)$ equation is of nonlinear limit circle type and also sufficient conditions that it is of nonlinear limit point type.
[M.Boudourides]
MSC 2000:
*34C05 Qualitative theory of some special solutions of ODE
34A34 Nonlinear ODE and systems, general
34A30 Linear ODE and systems

Keywords: limit cycle; limit circle; second order linear differential equations; nonlinear limit point

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