New results on the existence of periodic solutions to a p-Laplacian differential equation with a deviating argument

[摘要] By means of Mawhin's continuation theorem, a kind of p-Laplacian differential equation with a deviating argument as follows: (phi(p) (x'(t)))' = f(t, x(t), x (t - tau(t)), x'(t)) + e(t) is studied. Some new results on the existence of periodic solutions are obtained. The main results (Theorems 3.2 and 3.3) are all related to the deviating argument tau(t). Meanwhile, the degrees with respect to the variables x(0), x(1) of f(t, x(0), x(1), x(2)) are allowed to be grater than p - 1, which is different from the corresponding conditions of known literature. (c) 2007 Published by Elsevier Inc.

[发布日期] 2007-12-15

[关键词] periodic solution;mawhin's continuation theorem;deviating argument