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

Bartušek, Miroslav; Graef, John R.

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.

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