New results of periodic solutions for Rayleigh type pp-Laplacian equation with a variable coefficient ahead of the nonlinear term

In this paper, we consider the existence of periodic solutions for the Rayleigh type pp-Laplacian equation with a deviating argument (φp(x′(t)))′+f(x′(t))+β(t)g(x(t−τ(t)))=e(t).(φp(x′(t)))′+f(x′(t))+β(t)g(x(t−τ(t)))=e(t). The interest is that the function f(x)f(x) and the coefficient β(t)β(t) are allowed to change signs, which is different from the corresponding ones of known literature.