非线性高维共振椭圆系统解的存在性

摘要

By using the variational method and the Morse theory, combining with the calculation of critical group both at zero point and infinity point for the energy functional, we established the existence of solutions for some nonlinear resonant-dimension elliptic systems. A existed result of the two-dimension elliptic system zero boundary value resonant problem was generalized to ndimension resonance elliptic systems and the same conclusion was proved.%利用变分方法与Morse理论,结合能量泛函在零点与无穷远点临界群的计算,证明了一类非线性n维共振椭圆系统非平凡解的存在性.将二维椭圆系统零边值共振问题的一个已有结果推广到一般的n维共振椭圆系统,得到了同样的结论.