一类非线性基尔霍夫方程约束极小值点的存在性

The Existence of Constrained Minimizers for a Class of Nonlinear Kirchhoff Equations

主要考虑一类非线性基尔霍夫方程-(a+b∫_R^4|▽u|~2)Δu-|u|^(p-2) u=λu, u∈R^4,λ∈R.其中a,b>0为常数,p∈(2,3),结合泛函的强制性以及Brezis-Lieb引理,得到基尔霍夫方程的约束极小值点的存在性结果.

It is devoted to a class of nonlinear Kirchhoff equations-(a+b∫R4|▽u|2)△u-|u|^p-2u=λu,u∈R4,λ∈R.Where a,b>0 are constants.Combing the cocercivity of the functional and Brezi-Lieb lemma,we prove the existence of constrained minimizers for a class of nonlinear Kirchhoff equation.