带有组合非线性项的一类基尔霍夫方程径向解的存在性

Existence of Radial Solutions for Kirchhoff Problem with Combined Nonlinearities

为了研究一类带有组合非线性项的基尔霍夫方程的径向解的存在性,首先对方程中的V、K、f函数做出合理的假设,然后主要运用变分原理,先得到此方程相对应的能量泛函,之后证明了方程相对应的泛函满足PS条件且存在有界且收敛的PS子序列,最后利用山路引理得到该问题的径向解的存在性。

In order to study a type of Kirchhoff problem when the sublinear term is involved in nonlinearity, we firstly give some suitable assumptions about V,K,f functions. According to the variational method, its solutions can be regarded as critical points of the energy function. Supposing all the assumptions hold, then the energy function satisfies the PS condition and there exists a convergent PS subsequence which is bounded. Finally we use the mountain pass theorem to obtain the existence of one non-trivial solution.