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JIANG Weihua,ZHOU Cailian,LI Qingmin.Existence of solutions for differential equations systems with p-Laplacian at resonance[J].Journal of Hebei University of Science and Technology,2017,38(4):341-351
具有p-Laplacian算子的共振微分方程组解的存在性
Existence of solutions for differential equations systems with p-Laplacian at resonance
Received:October 01, 2016  Revised:May 10, 2017
DOI:10.7535/hbkd.2017yx04005
中文关键词:  常微分方程  边值问题  共振  Mawhin连续定理的拓展  p-Laplacian算子
英文关键词:ordinary differential equation  boundary value problem  resonance  the extension of Mawhin’s continuation theorem  p-Laplacian operator
基金项目:河北省自然科学基金(A2013208108)
Author NameAffiliationE-mail
JIANG Weihua School of Science Hebei University of Science and Technology Shijiazhuang jianghua64@163.com 
ZHOU Cailian School of Science Hebei University of Science and Technology Shijiazhuang  
LI Qingmin School of Science Hebei University of Science and Technology Shijiazhuang  
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中文摘要:
      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。
英文摘要:
      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.
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