By employing Mawhin’s continuation theorem, the existence of periodic solutions of the p-Laplacian differential equation with multiple deviating arguments (φp(x′(t)))′ + f(x(t))x′(t) + n ∑ j=1 βj(t)g(x(t− γj(t))) = e(t) under various assumptions are obtained. Keywords—periodic solution, Mawhin’s continuation theorem, deviating argument.

Sufficient conditions are given for a generalized Emden-Fowler equation with deviating argument to have nonoscillatory solutions with prescribed asymptotic behavior as t —> oo. The integrability condition on the nonlinear term requires only conditional convergence, supplemented by a condition on the order of convergence, which is automatically satisfied in some important special cases. The expo...

The half-linear difference equations with the deviating argument Δ an|Δxn| sgn Δxn bn|xn q| sgn xn q 0 , q ∈ Z are considered. We study the role of the deviating argument q, especially as regards the growth of the nonoscillatory solutions and the oscillation. Moreover, the problem of the existence of the intermediate solutions is completely resolved for the classical half-linear equation q 1 . ...