Bartušek, Miroslav; Graef, John R. The strong nonlinear limit-point/limit-circle properties for super-half-linear equations. (English) Zbl 1148.34023 Panam. Math. J. 17, No. 1, 25-38 (2007). Summary: The authors consider the nonlinear second order differential equation\[ a(t) |y'|^{p-1}y' + r(t)|y|^\lambda\text{sgn}\,y = 0,\tag{E} \]where \(p > 0\), \(\lambda > 0\), \(a(t) > 0\), \(r(t) > 0\), and \(\lambda > p\) (the super-halflinear case). They give necessary and sufficient conditions for equation (E) to be of the strong nonlinear limit-circle type and for (E) to be of the strong non-linear limit-point type. Examples illustrating the results are also included. Cited in 2 Documents MSC: 34B20 Weyl theory and its generalizations for ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations PDF BibTeX XML Cite \textit{M. Bartušek} and \textit{J. R. Graef}, Panam. Math. J. 17, No. 1, 25--38 (2007; Zbl 1148.34023) OpenURL