河北科技大学学报2025，Vol.46Issue(2)：175-185,11.DOI:10.7535/hbkd.2025yx02007
无穷区间上带p-Laplacian算子的分数阶q-差分方程的迭代正解
Iterative positive solutions for fractional q-difference equations with p-Laplacian operator on infinite intervals
摘要
Abstract
In order to enrich the basic theory of boundary value problems for fractional q-difference equations,the boundary value problems for a class of nonlinear fractional q-difference equations with p-Laplacian operator on infinite intervals were explored.Firstly,the Green function of the boundary value problem of linear fractional q-difference equation was calculated and its properties were studied.Secondly,the compactness criterion on infinite intervals was introduced and the integral operator on an abstract space was constructed.Thirdly,by selecting the initial value functions and using the monotone iterative technique,the existence of positive solutions for the boundary value problem were obtained.Finally,the validity of obtained results was verified through an example.The results show that when certain increasing condition is given to the nonlinear term f,the maximum and minimum positive solutions of the fractional q-difference equation can be obtained by establishing iterative sequences.The research results extend the existing relevant conclusions and provide theoretical reference for the further application of fractional q-difference equations in mathematics,physics and other fields.关键词
非线性泛函分析/分数阶q-差分方程/p-Laplacian算子/单调迭代技巧/无穷区间Key words
nonlinear functional analysis/fractional q-difference equations/p-Laplacian operator/monotone iterative tech-nique/infinite interval分类
数学引用本文复制引用
王菊芳,张金叶,禹长龙..无穷区间上带p-Laplacian算子的分数阶q-差分方程的迭代正解[J].河北科技大学学报,2025,46(2):175-185,11.基金项目
国家重点研发计划项目(2022YFB3806000) （2022YFB3806000）
国家自然科学基金(12272011) （12272011）
河北省自然科学基金(A2015208114) （A2015208114）
河北省教育厅基金(QN2017063) （QN2017063）
河北省研究生教育教学改革研究项目(YJG2024073) （YJG2024073）
河北科技大学教育教学改革研究项目(2020-ZD10) （2020-ZD10）
