Ricatti方程u″(t)-a(t)u(t)+b(t)u(t)~2=0存在非平凡同宿轨道

Existence of Nontrivial Homoclinic Orbits for Ricatti Equations u″(t)-a(t)u(t)+b(t)u(t)~2=0

利用临界点理论中的山路引理 ,证明了一类Ricatti方程u″(t) -a(t)u(t) +b(t)u(t) 2=0存在非平凡的同宿轨道 ,其中a(t) a0 >0 ,0 b(t) b0 ,但b(·)≠ 0 .

Using the Moutain Pass Lemma in critical point theory we have proved the existence of nontrivial homoclinic orbits for a class of Ricatti equations u″(t)-a(t)u(t)+b(t)u(t) 2=0 ,where a(t)a 0>0,0b(t)b 0, but b(·) ≠0.