渐近线性的Kirchhoff类方程变号解的存在性

Existence of a sign-changing solution for an asymptotically linear Kirchhoff equations

研究了全空间上一类径向对称的在无穷远点是渐近线性非线性项的自治的Kirchhoff方程,在适当条件下证明了Kirchhoff方程等价一个椭圆系统.再用各种分析技巧,得到了方程径向变号解的存在性结果。

In this paper,a class of radially symmetric autonomous Kirchhoff equations with asymptotic linearity at infinity is studied.Under the suitable conditions,we prove that the Kirchhoff equation is proved to be equivalent to the elliptic system.Furthermore,by using some analysis techniques,the existence result of a sign-changing solution is obtained.