论文摘要
我们首先研究下面半线性椭圆方程Dirichlet边值问题: 在次临界增长情况下,利用变分方法中的归约方法和三临界点定理,得到了方程至少有两个非平凡解。 其次,我们研究下面拟线性椭圆方程Dirichlet边值问题（p>1）: 在非线性项不再满足经典的Ambrosetti-Rabinowitz条件（简称（AR）条件）的渐近线性情况下,利用改进的山路引理,得到了方程正解的存在性和多解性。 最后,我们研究下列p（x）-Laplacian方程（p（x）>1）: 在超线性情况下,利用“喷泉定理”得到了无穷多解。
论文目录
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