2m阶Dirichlet边值问题解的存在性

Existence of solutions for 2m-order Dirichlet boundary value problem

利用无穷维Morse理论,研究了2 m阶非线性Dirichlet边值问题非平凡解的存在性.结果表明,在非线性项满足一定条件下,该边值问题至少存在两个非平凡解.

Using the Morse theory of infinite dimensional,the existence of nontrivial solutions for 2m-order nonlinear Dirichlet boundary value problem is discussed. The result shows that there exist at least two nontrivial solutions when the nonlinear term satisfies certain conditions.