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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.

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
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