New results on the existence and uniqueness of periodic solutions for Liénard type -Laplacian equation

By means of topological theory, a class of Liénard type p-Laplacian equation with a deviating argument of the form ( ϕ p ( x ′ ( t ) ) ) ′ + f ( x ( t ) ) x ′ ( t ) + β ( t ) g ( x ( t - τ ( t ) ) ) = e ( t ) is studied. The authors establish some criteria to guarantee the existence and uniqueness of periodic solutions for the above equation. It is meaningful that, compared with the corresponding ones in the known literature, the approaches used to estimate a prior bounds of periodic solutions are essentially new.