Multiplicity and dynamics of solutions of nonlinear differential equations

（1）对于一类带奇异项的非线性椭圆边值问题，利用最近发展起来的非光滑分析方法，得到了多解存在性的一些结果。这些结果是我们以前与比萨大学Claudio Saccon教授合作工作的改进。（2）对于带非齐次项的非线性椭圆边值问题，利用变分方法建立了多解存在性结果。结果保证了正解、负解和变号解的存在性。这项工作是与比萨大学的AnnaMaria Micheletti教授和罗马大学的Angela佩斯托亚合作完成的。

(1)For the nonlinear elliptic boundary value problem with singular tems, we used the method of nonsmooth analysis which has been developed recently, and got some results on the multiple existence of solutions. The results are improvement of our former joint work with Professor Claudio Saccon in Pisa University.(2)For the nonlinear elliptic boundary value problem with nonhomogeneous terms, we established the multiple existence results by using variational method. The results ensure the existence of positive, negative and sign changing solutions. This work was done under cooperation with Professor AnnaMaria Micheletti in Pisa University and Angela Pistoia in Rome University.