R^N上一类Kirchhoff型方程径向对称正解的存在性

Existence of Positive Radial Solution to a Class of Kirchhoff type Equation in R^N

该文讨论了一类能量泛函不属于C^1类的Kirchhoff型方程,这类方程与等离子体物理和激光传输理论有密切的联系.通过变量变换,该文首先将所讨论的方程变成了与之等价的能量泛函属于C^1类的方程.然后,通过构造合适的Banach空间,在适当的条件下运用变分方法证明了所讨论的方程存在径向对称正解.

In this paper,we discuss a class of Kirchhoff type equation whose energy function may not be of C^1 class.This equation is closely related to plasma physics and theories for propagation of laser beams.Using a change of variables,we get a new equivalent equation whose energy function is of C^1 class.Using a suitable Banach space and variational method,we prove that there is a positive radial solution to the given equation under proper conditions.