吴亚斌, 周文学, 宋学瑶. 带p-Laplacian算子的半线性分数阶脉冲微分方程解的存在性与唯一性[J]. 云南大学学报(自然科学版), 2023, 45(1): 9-17. doi: 10.7540/j.ynu.20220250
引用本文: 吴亚斌, 周文学, 宋学瑶. 带p-Laplacian算子的半线性分数阶脉冲微分方程解的存在性与唯一性[J]. 云南大学学报(自然科学版), 2023, 45(1): 9-17. doi: 10.7540/j.ynu.20220250
WU Ya-bin, ZHOU Wen-xue, SONG Xue-yao. Existence and uniqueness of solutions for semilinear fractional impulsive differential equation with p-Laplacian operator[J]. Journal of Yunnan University: Natural Sciences Edition, 2023, 45(1): 9-17. DOI: 10.7540/j.ynu.20220250
Citation: WU Ya-bin, ZHOU Wen-xue, SONG Xue-yao. Existence and uniqueness of solutions for semilinear fractional impulsive differential equation with p-Laplacian operator[J]. Journal of Yunnan University: Natural Sciences Edition, 2023, 45(1): 9-17. DOI: 10.7540/j.ynu.20220250

p-Laplacian算子的半线性分数阶脉冲微分方程解的存在性与唯一性

Existence and uniqueness of solutions for semilinear fractional impulsive differential equation with p-Laplacian operator

  • 摘要: 研究了一类带p-Laplacian算子的半线性分数阶脉冲微分方程反周期边值问题. 首先将分数阶微分方程转化为等价的积分方程,然后通过使用Schauder不动点定理、Schaefer不动点定理及Banach压缩映射原理得到了边值问题解的存在性与唯一性,最后举例验证主要结果的合理性.

     

    Abstract: We consider a class of anti-periodic boundary value problems of semilinear fractional impulsive differential equation with p-Laplacian operator. Firstly, the fractional differential equation is transfromed into equivalent integral equation. Secondly, we are devoted to the existence and uniqueness of solution for the boundary value problem by utilizing Schauder fixed-point theorem, Schaefer's fixed-point theorem, and Banach compression mapping principle. Finally, examples are given to illustrate the main results.

     

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