一类具有偏差变元的p-Laplacian Liénard型方程在吸引奇性条件下周期解的存在性

摘要

该文考虑了一类具有偏差变元的奇性p-Laplacian Lienard型方程 (ψp(xt(t)))t + f(x(t))xt(t) + g(t, x(t ― σ(t))) = e(t),其中g(x)在原点处具有吸引奇性.通过应用Manasevich-Mawhin连续定理和一些分析方法, 证明了这个方程周期解的存在性.%In this paper, we consider a kind of p-Laplacian singular Lienard equation with time-dependent deviating argument (ψp(xt(t)))t + f(x(t))xt(t) + g(t, x(t ― σ(t))) = e(t), where g has a attractive singularity at x = 0. By applications of Manasevich-Mawhin continuation theorem and some analysis skills, sufficient conditions for the existence of periodic solution is established.