一类含p-Laplace算子的奇异拟线性问题解的多重性

Multiplicity of Solutions of a Class of Singular Quasilinear Problems Involving p-Laplacian

本文结合上下解技巧和极大极小方法研究了一类奇异拟线性椭圆型方程解的存在性和多重性。首先,在赋予非线性项和奇异项合理的假设条件下,得到了该问题非平凡解的存在性;其次,增强假设条件并运用山路引理,我们获得了该问题第二个解。

In this paper we combine sub-supersolution technique and minimax methods to study the existence and multiplicity of solutions for a class of singular quasilinear elliptic equations. Firstly, by suitable hypotheses on the nonlinearity term and singular term, we obtain the existence of nontrivial solutions. Furthermore, by strengthening the hypotheses and applying the Mountain Pass Theorem, we show the existence of a second solution.