含有对数非线性项的p-Laplace方程的多重解

The Multiple Solutions of p-Laplace Equation with Logarithmic Nonlinearity

主要通过变分方法研究了有界区域上含有变号权函数和对数非线性项的一类p-Laplace方程Dirichlet边值问题的多解性.通过分解能量泛函的Nehari流形,利用对数Sobolev不等式,极小化序列方法及相关知识证明了能量泛函至少存在两个非零极小元,从而证明了问题至少存在两个非平凡解.

In this paper, we study the multiple solutions of p-Laplace equation Dirichlet boundary-value problem with sign-changing weight function and logarithmic nonlinearity on the bounded domain by using variational methods. By decomposition the Nehari manifold of the energy functional and then use the logarithmic Sobolev inequality, minimizing sequence method and related knowledge, it was proved that energy functional has two nonzero minimal elements, thus this problem has at least two nontrivial solutions.