On existence of nonoscillatory solutions in forced nonlinear differential equations
The author gives sufficient conditions for the existence of a nonoscillatory solution to the equation \[ \frac{1}{p_ n(t)}\frac{d}{dt}\frac{1}{p_{n- 1}(t)}\frac{d}{dt}...\frac{d}{dt}(\frac{1}{p_ 0(t)}y(t))+F(t,y(t))=f(t) \] (p\({}_ i,f\) continuous on [a,\(\infty)\), \(a>0\), \(p_ i(t)>0\), \(F: R\times R\to R\) continuous, vF(u,v)\(\geq 0\) and F(u,.) increasing) and shows that his conditions are in a certain sense minimal.
scientific article; zbMATH DE number 3942008