带有奇异和变号位势Kirchhoff型方程的多重正解

Multiple Positive Solutions of Kirchhoff Type Equations with Singular and Sign-Changing Potential

作者研究一类带有奇异和变号位势的Kirchhoff型方程Neumann边值问题在次临界情况下,对于参数λ>0足够小时,首先运用扰动方法解决含奇异项所对应的泛函在零点处不可微的问题,其次对空间进行分解,证明了该问题的能量泛函满足山路结构和PS条件;最后通过Ekeland变分原理和山路引理得到了两个正解的存在性。

In this paper,we studied a class of Neumann boundary value problems for Kirchhoff type equations with singular and signchanging potentials.We established the existence of two distinct positive solutions for small values of a parameterλ>0in a subcritical case.Firstly,the perturbation method was used to solve the problem that the functional corresponding to the singular term was not dif-ferentiable at zero point.Secondly,the decomposition process for the underlying space was proved that the energy functional of the prob-lem satisfied the mountain pass geometry and PS condition.Finally,the existence of two positive solutions was obtained by Ekeland’s variational principle and mountain pass lemma.