一类Kirchhoff型方程正解的存在性

Existence of positive solutions for Kirchhoff type equation

变分法、临界点理论利用本文考虑具有Dirichlet边值条件的非线性Kirchhoff型问题-（a＋b∫Ω｜Δu｜~2dx）Δu=f（x,u）,在非线性项f适当的假设条件下给出了该Kirchhoff型问题至少存在一个正解.

We show that the following nonlinear Kirchhoff type problem -（a＋b∫Ω｜Δu｜~2dx）Δu=f（x,u） ~with Dirichlet boundary value has at least one positive solution under suitable assumptions on the nonlinear term f. The main tools are variational method, critical point theory and some analysis ~ech niques.