Periodic Solutions for Duffing Type p -Laplacian Equation with Multiple Constant Delays

Abstract

Using inequality techniques and coincidence degree theory, new results are provided concerning the existence and uniqueness of periodic solutions for the Duffing type $p$-Laplacian equation with multiple constant delays of the form ${\left({\phi }_p\left(x^{\prime }\left(t\right)\right)\right)}^{\prime }+C{x}^{\prime }\left(t\right)+g_0\left(t,x\left(t\right)\right)+{\sum }_{k=1}^n{g}_k\left(t,x\left(t-{\tau }_k\right)\right)=e\left(t\right).$ Moreover, an example is provided to illustrate the effectiveness of the results in this paper.