E. M. Elabbasy
Department of Mathematics,
Faculty of Science,
Mansoura University, Mansoura,
35516, Egypt.
A. A. S. Zaghrout
Department of Mathematics,
Faculty of Science,
AI-Azhar University,
Nasr-city, P.O. Box 9019.
11765 Cairo, Egypt.
H. M. Elshebany
Department of Mathematics,
Faculty of Science,
AI-Azhar University,
Nasr-city, P.O. Box 9019.
11765 Cairo, Egypt.
By using averaging functions, several new oscillation criteria are established for the half-linear damped differential equation
and the more general equation
where where p,q ,r:[t0, ∞)->R and ψ,g: R->R are continuous, r(t)>0, p(t)≥0 and ψ(x)>0, xg(x)>0 for x≠0, α>1 a fixed real number. Our results generalize and extend some known oscillation criteria in the literature