Periodic solutions for a Rayleigh type p-Laplacian equation with sign-variable coefficient of nonlinear term

摘要

As p-Laplacian equations have been widely applied in the field of fluid mechanics and nonlinear elastic mechanics, it is necessary to investigate the periodic solutions of functional differential equations involving the scalar p-Laplacian. By using Lu’s continuation theorem, which is an extension of Manásevich–Mawhin, we study the existence of periodic solutions for a Rayleigh type p-Laplacian equation(φp(x′(t)))′+f(x′(t))+g1(x(t-τ1(t,|x|∞)))+β(t)g2(x(t-τ2(t,|x|∞)))=e(t).It is significant that the growth degree with respect to the variable u in g1(u) is allowed to be greater than p-1 and the coefficient β(t) of g2(x(t-τ2(t,|x|∞))) can change sign in this paper, which could be achieved rarely in the previous literature.