CAJ | 학술논문

研究了二阶非自治离散Hamilton系统多重变号周期解的存在性问题.在非线性项是奇函数的条件下,将这类Hamilton系统的变号周期解转化为定义在一个适当空间上泛函的临界点,然后利用Morse理论中的三临界点定理,建立了此类系统至少2个变号周期解的存在性结果,并举例说明了所获得的主要结果是有效的.
연구료이계비자치리산Hamilton계통다중변호주기해적존재성문제.재비선성항시기함수적조건하,장저류Hamilton계통적변호주기해전화위정의재일개괄당공간상범함적림계점,연후이용Morse이론중적삼림계점정리,건립료차류계통지소2개변호주기해적존재성결과,병거례설명료소획득적주요결과시유효적.
In this paper, we investigate the existence of multiple sign-changing periodic solutions for second order non-autonomous discrete Hamiltonian system. Under the condition that the nonlinearity is an odd function, we convert sign-changing periodic solutions of the system into the critical points of a functional defined on a proper space, and prove that there exist at least two different sign-changing periodic solutions. The approach used here is based on a 3 critical points theorem in the Morse theory. An illustrative example is given to demonstrate the effectiveness of the obtained main result.