Nonoscillation of second-order nonhomogeneous differential equations
In this paper sufficient conditions are obtained for nonoscillation of all solutions of \((r(t)y')'-p(t)y=f(t)\) and all bounded solutions of \((r(t)y')'-p(t)y^{\gamma}=f(t),\) where r,p and f are real-valued continuous functions on \([0,\infty)\) such that \(r(t)>0\) and p(t) and f(t) are allowed to change sign and \(\gamma>0\) is a quotient of odd integers. In case of the linear nonhomogeneous equations this is achieved by the employment of a transformation. Recently the authors have obtained some results concerning asymptotic behaviour of nonoscillatory solutions of such equations.
scientific article; zbMATH DE number 3865735