## 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.

### 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