Periodic solutions for fourth-order p-Laplacian functional differential equations with sign-variable coefficient - Jiaying Liu; Wenbin Liu; Bingzhuo Liu (Electronic Journal of Differential Equations, 2013)
Using the theory of coincidence degree, we show the existence of periodic solutions to the fourth-order p-Laplacian differential equations of Lienard-type $$ φ_p(x''))''+f(x(t))x'(t)+α(t)g_1(x(t-τ_1(t,x(t)))) +β(t)g_2(x(t-τ_1(t,x(t))))=p(t). $$ The rate of growth of $g_1(u)$ with respect to the variable u is allowed to be greater than p-1, and the coefficient $β (t)$ is allowed to change sign.