Linearization of second-order superlinear oscillation theorems
The authors present comparison theorems for oscillation of second-order superlinear differential equations. The main results involve the comparison with related linear and half-linear second-order differential equations, so that the known oscillation theorems from literature can be employed directly. A typical result is the following one: Assume that \[ \int_{t_0}^{\infty} a^{-1/\alpha}(s)ds = \infty \] and \[ f^{(1/\alpha)-1}(x)f'(x)\geq k>0, \] for \(x\neq 0\), where \(k\) is a constant. If the half-linear equation \[ (a(t)| y'(t)| ^{\alpha-1}y'(t))'+\left(\frac k{\alpha}\right)q(t)| y(t)| ^{\alpha-1}y(t)=0 \] is oscillatory, then the superlinear equation \[ (a(t)| x'(t)| ^{\alpha-1}x'(t))'+q(t)f(x(t))=0 \] is also oscillatory.
scientific article; zbMATH DE number 2137118
scientific article