Graef, John R. Limit circle type results for sublinear equations. (English) Zbl 0535.34024 Pac. J. Math. 104, 85-94 (1983). 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 \(\int^{\infty}_{t_ 0}x(u)f(x(u))du<\infty\) 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 \(f(x)=x^{\gamma}\), \(0<\gamma \leq 1\). 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. Reviewer: M.Boudourides Cited in 7 Documents MSC: 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 34A30 Linear ordinary differential equations and systems Keywords:limit cycle; limit circle; second order linear differential equations; nonlinear limit point PDF BibTeX XML Cite \textit{J. R. Graef}, Pac. J. Math. 104, 85--94 (1983; Zbl 0535.34024) Full Text: DOI