Existence of solutions for 2mth-order periodic boundary value problems
Existence of solutions for 2mth-order periodic boundary value problems
复制标题
DOI：
10.1016/j.amc.2011.06.052
复制
发表时间：
2011-11
期刊：
影响因子：
--
通讯作者：
Xiaojing Feng;P. Niu;Qianqiao Guo
中科院分区：
文献类型：
--
作者：
Xiaojing Feng;P. Niu;Qianqiao Guo
研究了一类2 m阶微分方程周期边值问题：（-1）mu（2 m）（t）+∑i= 1 m（-1）m-iaiu（2（m-i））（t）=f（t，u（t）），其中u（i）（0）=u（i）（1），i= 0，1，.，2 m −1，其中f∈C1（[0，1]×R1，R1），ai∈R1，i= 1，2，.，m.利用莫尔斯理论，我们对f施加一定的条件，分别保证问题至少有一个非平凡解、两个非平凡解和无穷多个解.
In this paper, the existence results of solutions are obtained for the 2mth-order differential equation periodic boundary value problem: (-1)mu(2m)(t)+∑i=1m(-1)m-iaiu(2(m-i))(t)=f(t,u(t)) for all t∈[0,1] with u(i)(0)=u(i)(1), i=0,1,…,2m−1, where f∈C1([0,1]×R1,R1),ai∈R1,i=1,2,…,m. By using the Morse theory, we impose certain conditions on f which are able to guarantee that the problem has at least one nontrivial solution, two nontrivial solutions and infinitely many solutions, separately.