化简二次曲面方程的矩阵方法

利用矩阵运算，结合向量的数量积和外积，介绍一种化二次曲面一般方程为标准形的简便方法

一类超线性椭圆方程的无穷多解

本文研究了一类超线性椭圆方程, 这里的非线性项是奇的我们不需要假设Ambrosetti-Rabinowitz条件, 得到了无穷多个大能量解的存在性我们的结论推广了邹文明最近的结果 ,国家自然科学基金973资助项目(2178200)北京市自然科学基金资助项目(1022003

RN 中一类带p-凹凸非线性项的拟线性椭圆方程的无穷可解性

在适当条件下, 得到RN中的p-Laplace 方程的无穷多解的存在性, 其中: p < N , 1 < q < p < s < p 3 ≡N p/(N - p ).国家自然科学基金(19971037) 和甘肃省自然科学基金(ZS9912A 25) 资助项

Multiple solutions for elliptic resonant problems

National Natural Science Foundation of China [10601041]Two non-trivial solutions for semilinear elliptic resonant problems are obtained via the Lyapunov Schmidt reduction and the three-critical-points theorem. The difficulty that the variational functional does note satisfy the Palais Smale condition is overcome by taking advantage of the reduction and a careful analysis of the reduced functional

Nontrivial solutions for elliptic resonant problems

Nontrivial solutions for elliptic resonant problems are obtained via Morse theory. To compute the critical groups at infinity of the relevant functional, we propose a new approach by combining the homotopy and reduction methods, and the Alexander Duality Theorem. (C) 2008 Elsevier Ltd. All rights reserved

Remarks on multiple solutions for elliptic resonant problems

We obtain four nontrivial solutions for an elliptic resonant problem via Morse theory and Lyapunov-Schmidt reduction method. Our result improves some recent works. (c) 2007 Published by Elsevier Inc

Multiple Periodic Solutions for Nonlinear Difference Equations

用变分方法得到一类非线性差分方程多重周期解的存在性.我们的结果推广了Cai, Yu和Guo[Comput.Math.Appl.,52(2006),1630-1647]的结果,并且这里给出的证明显著地简化了.Multiple solutions for a class of nonlinear difference equations are obtained by variational methods. Our results generalize a recent result of Cai,Yu and Guo[Comput.Math.Appl.,52(2006),1630-1647],and the argument here is considerably simpler.Supported by National Natural Science Foundation of China(10601041) and by NCETF

Homology of saddle point reduction and applications to resonant elliptic systems

NSFC [11071237, 11171204]; RFDP [20094402110001]In the setting of saddle point reduction, we prove that the critical groups of the original functional and the reduced functional are isomorphic. As application, we obtain two nontrivial solutions for elliptic gradient systems which may be resonant both at the origin and at infinity. The difficulty that the variational functional does not satisfy the Palais-Smale condition is overcame by taking advantage of saddle point reduction. Our abstract results on critical groups are crucial. (C) 2012 Elsevier Ltd. All rights reserved

Nontrivial solutions of superlinear p-Laplacian equations

We consider p-Laplacian equations on a bounded domain, where the nonlinearity is superlinear but dose not satisfy the usual Ambrosetti-Rabinowitz condition near infinity, or its dual version near zero. Nontrivial solutions are obtained by computing the critical groups and Morse theory. (c) 2008 Elsevier Inc. All rights reserved

Generalized saddle point theorem and asymptotically linear problems with periodic potential

National Natural Science Foundation of China [11171204]; Fundamental Research Funds for the Central Universities; GDNSF [S2012010010038]We prove a critical point theorem, which is an infinite dimensional generalization of the classical saddle point theorem of P. H. Rabinowitz. As an application we obtain solution of asymptotically linear Schrodinger equations with periodic potential. (C) 2013 Elsevier Ltd. All rights reserved