带有凹凸非线性项的Kirchhoff型方程解的多重性

Multiplicity of Solutions for Kirchhoff Equation with Concave and Convex Nonlinearities

利用集中紧性原理和对偶喷泉定理,研究了一类带有凹凸非线性项的Kirchhoff方程{-(a+b∫Ω|▽u|~2dx )Δu=|u|~4u+μ|u|^(q-2)u x∈Ω u=0 x∈?Ω获得了该方程有无穷多个解.其中Ω为R^3中边界光滑的有界开集,且a,b>0,1<q <2,μ>0.

In this paper,we study a class of Kirchhoff equation {-（a＋b∫Ω｜▽u｜^2dx ）Δu=｜u｜~4u＋μ｜u｜^q-2u x∈Ω u=0 x∈δΩ with concave and convex nonlinearities,where Ω R^3 is a smooth bounded domain with a,b〉0,1〈q〈2,μ〉0.By means of the concentration compactness principle and a dual fountain theorem,we obtain the multiplicity of solutions about this equation.