具有p-Laplacian算子的共振微分方程组解的存在性

摘要

为了研究具有非线性分数阶微分算子的微分方程共振边值问题解的存在性,引入了推广的Mawhin 连续定理,通过定义合适的Banach空间及范数,给出恰当的算子,运用Mawhin 连续定理的拓展,研究了具有p-Laplacian 算子的分数阶共振微分方程组边值问题解的存在性.通过举例验证了所得结论的正确性.所得结论是共振边值问题现有成果的推广和一般化,对进一步研究具有一定参考价值.%In order to study the existence of solutions for boundary value problems at resonance with nonlinear fractional differential operator, a generalization of Mawhin's continuous theorem is introduced.By defining suitable Banach space and norm, constructing the proper operators and using the extension of Mawhin continuation theorem, the existence of solutions for fractional differential equations systems boundary value problem with p-Laplacian at resonance is studied.An example is given to illustrate the main results.The results are the improvement and generalization of some existing results of boundary value problems at resonance.