Nonoscillation theorems for second order nonlinear differential equations

We prove nonoscillation theorems for the second order Emden-Fowler equation (E): y " + a(x)\y\(gamma-1) y = 0, gamma > 0, where a(x) is an element of C(0; infinity) and gamma not equal 1. It is shown that when x((gamma+3)/2+d elta)a(x) is nondecreasing for any delta > 0 and is bounded above, then (E) is nonoscillatory. This improves a well-known result of Belohorec in the s ublinear case, i.e. when 0 < gamma < 1 and 0 < delta < (1-gamma)/2.