具p-Laplace算子分数阶非齐次边值问题正解的存在性

doi:10.6040/j.issn.1671-9352.0.2018.302

摘要/Abstract

摘要： 研究一类带有扰动参数以及p-Laplace算子的分数阶微分方程积分边值问题正解的存在性。根据积分核的性质,利用范数形式的锥拉伸与锥压缩不动点定理,以及超线性与次线性条件,得到边值问题正解的存在性与不存在性的充分条件,所得结论体现了参数对正解存在性的影响。最后,给出了例子以说明所得结果的合理性。

关键词: 分数阶微分方程, p-Laplace算子, 扰动参数, 不动点定理, 正解

Abstract: We study the existence of positive solutions for integral boundary value problem of fractional p-Laplacian equation with disturbance parameters. According to the properties of integral kernel and using the cone expansion and cone compression fixed point theorem and the super-linear and sub-linear conditions, the sufficient conditions of existence and nonexistence of positive solutions for the boundary value problem are obtained. The conclusions show the impact of parameters on the existence of positive solutions. Finally, we give some examples to illustrate our main results.

Key words: fractional differential equation, p-Laplacian operator, disturbance parameter, fixed point theorem, positive solution

中图分类号:

O175.8

宋君秋,贾梅,刘锡平,李琳. 具p-Laplace算子分数阶非齐次边值问题正解的存在性[J]. 《山东大学学报(理学版)》, 2019, 54(10): 57-66.

SONG Jun-qiu, JIA Mei, LIU Xi-ping, LI Lin. Existence of positive solutions for fractional nonhomogeneous boundary value problem with p-Laplacian[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(10): 57-66.

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