一类Kirchhoff型方程基态解的存在性

The Existence of Ground-State Solutions to a Class of Kirchhoff Type Equations

研究了一类Kirchhoff型方程基态解的存在性.非线性项f(u)形如|u|^(p-2 )u(4<p<6)的一类Kirchhoff型方程已经被广泛研究,但是由于非线性项f(u)形如|u|^(p-2 )u(2<p<6)不满足AmbrosettiRabinowitz条件,故证明Palais-Smale序列的有界性成为证明基态解存在性的主要困难.本文运用经典的变分方法将山路定理结合Pohozaev恒等式证明了,在某种条件下即当非线性项f(u)形如|u|^(p-2 )u(2<p<6)时,一类Kirchhoff型方程基态解的存在性.

An explotation was made on the existence of ground-state solutions for a class of Kirchhoff type equations. Kirchhoff type equations with nonlinearity f（u）～｜u｜^p-2（2〈p〈6） has been studied ex- tensively. As f（u）～｜u｜^p-2（2〈p〈6） does not satisfy the Ambrosetti-Rabinowitz condition, the boundedness of Palais-Smale sequence becomes a major difficulty in proving the existence of ground-state solutions. According to the classical variational principle, the mountain-pass theorem and Pohozaev＇s i- dentity were used to show the existence of ground-state solutions for a class of Kirchhoff type equations under certain assumptions on the nonlinearity f（u）, i.e. f（u） ｜u｜^p-2（2〈p〈6）.