摘要
本文主要研究2n阶两点边值问题的多重非平凡解的存在性．利用不动点指数理论和Leray-schauder度,在一般的非线性条件下,证明了2n阶两点边值问题至少有六个非平凡解的存在性．而且,如果非线性项是奇函数,则至少有八个非平凡解的存在．
In this paper, we study the existence and multiplicity of nontrivial solutions for the 2nth-order two-point boundary value problems. Making use of the theory of fixed point index in cone and Leray-Schauder degree, under general conditions on nonlinearity, we prove that there exist at least six different nontrivial solutions for the 2nth-order two-point boundary value problems. Furthermore, if the nonlinearity is odd, we obtain that there exist at least eight different nontrivial solutions.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2007年第2期347-356,共10页
Acta Mathematica Sinica：Chinese Series
基金
山东省自然科学基金(Y2004A01)
山东省教育厅资助项目(J05A07)
