共振双相问题的周期解的存在性
Existence of Periodic Solution of Resonant Double Phase Problem
DOI: 10.12677/PM.2023.134079, PDF,   
作者: 杨艺豪, 鄢兴业：江西理工大学理学院，江西 赣州
关键词: 双相问题；共振；周期解；山路引理；Double Phase Problem； Resonance； Periodic Solution； Mountain Pass Lemma
摘要: 本文研究了一维双相问题在共振条件下周期解的存在性。利用山路定理和变分法证明一维的双相问题在相关方程的第一特征值λ1处共振，且非线性项f(x,u)满足一些局部非线性条件时，存在至少一个周期解。
Abstract: In this paper, the existence of periodic solutions for one-dimensional double phase problem under resonance conditions is studied. By using the mountain pass theorem and the variational method, it is proved that the one-dimensional double phase problem resonates at the first eigenvalue λ1 of the correlation equation, and there is at least one periodic solution when the nonlinear term f(x,u) satisfies some local nonlinear conditions.
文章引用：杨艺豪, 鄢兴业. 共振双相问题的周期解的存在性[J]. 理论数学, 2023, 13(4): 759-765. https://doi.org/10.12677/PM.2023.134079

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