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Limit circle type results for sublinear equations. (English) Zbl 0535.34024
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 t 0 x(u)f(x(u))du< and of nonlinear limit point type otherwise (this definition generalizes 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 γ , 0<γ1. 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.
Reviewer: M.Boudourides
MSC:
34C05Location of integral curves, singular points, limit cycles (ODE)
34A34Nonlinear ODE and systems, general
34A30Linear ODE and systems, general