共振条件下椭圆方程的两个非零解

Two Untrivial Solutions for Elliptic Equation under Resonance Condition

研究共振条件下的一类椭圆边值问题,利用临界点理论中的Morse理论方法,通过计算零点和无穷远处的临界群,根据Morse不等式,得到该方程两个非零解的存在性.

Variational method is one of the powerful tools to solve differential equations, and critical point theory is usually to study the existence of untrivial solutions for Dirichlet boundary value problems. In this paper, by the use of the Morse method in critical point theory, the calculation of the critical group in zero and infinity, and the Morse inequality, the existence of the two untrivial solutions for elliptic equation is verified.