一类拟线性p-KirchhofF型方程多解的存在性

Multiple Solutions for a Class of Quasilinear p-Kirchhoff Equation

研究一类无界区域上的p-Kirchhoff型椭圆问题■弱解的存在性.其中Ω是R^N(N>1)中一边界光滑的有界区域的外部区域.1<p<N,λ∈R^1\{0}是参数,权函数V(x),f(x),g(x)满足一定的条件.利用Nehari流形和纤维环映射方法证明了此问题至少存在两个弱解.

In this paper,we study the existence of nontrivial solutions for a class of quasilinear p-Kirchhoff equation■whereΩis the complement of a smooth bounded domain in R^N(N≥3).1<p<N andλ∈R^1\{0}is a parameter.The weight functions V(x),f(x)and g(x)satisfy some conditions.We will prove that the problem has at least two solutions by using the Nehari manifold and fibering maps associated with the Euler function for this problem.