# RANGE OF PARAMETER FOR THE EXISTENCE OF PERIODIC SOLUTIONS OF LI$\'{E}$NARD DIFFERENTIAL EQUATIONS

• Lee, Yong-Hoon (Department of Mathematics, Pusan National University, Pusan 609-735)
• Published : 1995.08.01

#### Abstract

In 1986, Fabry, Mawhin and Nkashama [1] have considered periodic solutios for Lienard equation $$(1_s) x" + f(x)x' + g(t,x) = s,$$ where s is a real parameter, f and g are continuous functions, and g is $2\pi$-periodic in t and have proved that if $$(H) lim_{\midx\mid\to\infty} g(t,x) = \infty uniformly in t \in [0,2\pi],$$ there exists $s_1 \in R$ such that $(1_s)$ has no $2\pi$periodic solution if $s< s_1$, and at least one $2\pi$-periodic solution if $s = s_1$, and at least two $2\pi$-periodic solutions if $s > s_1$.s_1\$.