Oscillatory and asymptotic behavior of higher order differential equations with deviating arguments (Q2266157)

We study the oscillatory and asymptotic behavior of the solutions of the higher order functional differential equation \((1)\quad [r(t)x^{(n- \nu)}(t)]^{(\nu)}+\delta p(t)f(x[g(t)])=0\) where \(1\leq \nu \leq n-1\) and \(\delta =\pm 1\). Many other authors have considered various special cases of (1) especially when \(\delta =+1\) and r(t)\(\equiv 1\). In particular, equation (1) includes as special cases the well known second order Emden- Fowler and Thomas-Fermi equations which occur in various applications. The types of integral conditions imposed on p(t) in this paper differ from those previously required by other authors. Also, since \(\nu\) can be any integer satisfying \(1\leq \nu \leq n-1\), equation (1) can have a variety of possible middle terms.