摘要：The efficient conditions guaranteeing the existence of positive T-periodic solution to the p-Laplacian–Liénard equation ( ϕ p ( x ′ ( t ) ) ) ′ + f ( x ( t ) ) x ′ ( t ) + α 1 ( t ) g ( x ( t ) ) = α 2 ( t ) x μ ( t ) , $$\bigl(\phi _{p}\bigl(x'(t)\bigr) \bigr)'+f \bigl(x(t)\bigr)x'(t)+\alpha _)(t)g\bigl(x(t)\bigr)= \frac{ \alpha _,(t)}{x^{\mu }(t)}, $$ are established in this paper. Here ϕ p ( s ) = | s | p − 2 s $\phi _{p}(s)=|s|^{p-2}s$ , p > 1 $p>1$ , α 1 , α 2 ∈ L ( [ 0 , T ] , R ) $\alpha _),\alpha _,\in L([0,T],{R}) $ , f ∈ C ( R + , R ) $f\in C({R}_{+},{R})$ ( R + ${R} _{+}$ stands for positive real numbers) with a singularity at x = 0 $x=0$ , g ( x ) $g(x)$ is continuous on ( 0 ; + ∞ ) $(0;+\infty )$ , μ is a constant with μ > 0 $\mu >0$ , the signs of α 1 $\alpha _)$ and α 2 $\alpha _, $ are allowed to change. The approach is based on the continuation theorem for p-Laplacian-like nonlinear systems obtained by Manásevich and Mawhin in (J. Differ. Equ. 145:367–393, 1998).
