摘要：In this paper, the problem of a homoclinic solution is studied for the prescribed mean curvature Liénard equation ( u ′ ( t ) 1 + ( u ′ ( t ) ) 2 ) ′ + f ( u ( t ) ) u ′ ( t ) + g ( u ( t ) ) = p ( t ) $(\frac{u'(t)}{\sqrt{1+(u'(t))^,}})'+f(u(t))u'(t)+g(u(t))=p(t)$ , where f ∈ C ( R , R ) $f\in C(R,R)$ , g ∈ C 1 ( R , R ) $g\in C^)(R,R)$ , and p ∈ C ( R , R ) $p\in C(R,R)$ . Under some conditions, the author obtains the result that the equation has at least one nontrivial homoclinic solution for p ( t ) ≢ 0 $p(t)\not\equiv0$ , and the equation has no nontrivial homoclinic solution for p ( t ) ≡ 0 $p(t)\equiv0$ . The arguments are based upon Mawhin’s continuation theorem.
