摘要
应用临界点理论中的山路引理,研究了一类四阶非线性差分方程周期解和次调和解的存在性问题.通过把方程解的存在性转化为某个泛函临界点的存在性,获得了一类四阶非线性差分方程周期解和次调和解的存在性和多重性的一些充分条件,给出周期解和次调和解的存在性和多重性准则.
By using the notable Mountain Pass Lemma of critical point theory, some sufficient condi-tions for the existence and multiplicity of periodic and subharmonic solutions to a class of fourth-order non-linear difference equations are obtained. The proof is based on the Mountain Pass Lemma in combination with variational technique. A practicable method to solve the existence and multiplicity of periodic and sub-harmonic solutions for fourth-order nonlinear forward and backward difference equations is given.
出处
《内蒙古师范大学学报（自然科学汉文版）》
CAS
北大核心
2013年第3期254-258,共5页
Journal of Inner Mongolia Normal University(Natural Science Edition)
基金
国家自然科学基金资助项目(11171078)
高等学校博士学科点专项科研基金(20114410110002)
广东省教育科学"十一五"规划课题项目(2010tjk074)
关键词
动力系统
四阶差分方程
周期解和次调和解
山路引理
离散变分理论
dynamic system
fourth-order difference equation
periodic and subharmonic solutions
Mountain Pass Lemma
discrete variational theory
