一类满足Costa非二次型条件六阶半线性微分方程同宿轨道解的存在性研究

Existence of Homoclinic Solutions of a Class of Semilinear Sixth-order Differential Equations with Costa Nonquadratic Potentials

本文运用山路引理研究了一类满足Costa非二次型条件的六阶半线性微分方程u(vi)-Au(iv)+Bun-Cu-Fn(x,u)=0同宿轨道解的存在性,其中A>0,B>0,C>0.。

In this paper we apply Mountain-Pass Theorem to study the existence of homoclinic solution for a class of semilinear sixth-order differential equations with Costa nonquadratic potentials () () '' (,) 0 vi iv u u ? Au + Bu ? Cu ? F x u= Where A > 0,B > 0,C>0.