Properties of Kneser's solution for half-linear third order neutral differential equations
The authors consider the third-order neutral differential equation of advanced type \[ (a(t)(b(t)(z'(t))^\alpha)')'+q(t)y^\alpha(t)=0, \] where \(\alpha\) is a ratio of odd positive integers, \(z(t)=y(t)+p(t)y(\sigma(t))\), \(\sigma(t)\geq t\), \(a,b,\sigma,q\) are continuous and positive functions, and some other hypotheses are assumed. Sufficient conditions are established which guarantee that all nonoscillatory solutions of this equation are of Kneser type, i.e., \(y(t)>0,y'(t)<0,((y'(t))^\alpha),((y'(t))^\alpha)''<0\) for large \(t\). In addition, estimates for these solutions are derived.
scientific article; zbMATH DE number 6837896