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The strong nonlinear limit-point/limit-circle properties for super-half-linear equations. (English) Zbl 1148.34023
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.

34B20Weyl theory and its generalizations
34C11Qualitative theory of solutions of ODE: growth, boundedness
34D05Asymptotic stability of ODE