مشخصات پژوهش

In this work we study the existence of homoclinic orbits of the planer system of Li´enard type 𝑥˙ = 𝐾(𝑦 − 𝐹(𝑥)), 𝑦˙ = −𝑔(𝑥), where 𝐾 is strictly increasing and 𝐾(±∞) = ±∞. We present sufficient and necessary conditions for this system to have a positive and a negative semiorbit which starts at a point on the curve 𝑦 = 𝐹(𝑥) and approaches the origin without intersecting the 𝑥-axes. The conditions obtained are very sharp.