分数阶变系数边值问题非平凡弱解的存在性

doi:10.6040/j.issn.1671-9352.0.2021.058

摘要/Abstract

摘要： 利用环绕定理和山路定理,研究一类分数阶变系数Dirichlet边值问题非平凡弱解的存在性。在变分框架下,此类问题的研究多是需要Ambrosetti-Rabinowtiz条件,给出了比Ambrosetti-Rabinowtiz条件弱的条件。

关键词: 分数阶微分方程, 变系数, 弱解, 变分法

Abstract: The existence of nontrivial weak solutions for a class of fractional Dirichlet boundary value problems with variable coefficients is studied by using Linking theorem and Mountain pass theorem. Under the variational framework, Ambrosetti-Rabinowtiz condition is mostly needed for the study of such problems, and the weaker condition than Ambrosetti-Rabinowtiz condition is given.

Key words: fractional differential equation, variable coefficient, weak solution, variational method

中图分类号:

O175.14

薛婷婷,徐燕,刘晓平. 分数阶变系数边值问题非平凡弱解的存在性[J]. 《山东大学学报(理学版)》, 2021, 56(12): 45-51.

XUE Ting-ting, XU Yan, LIU Xiao-ping. Existence of nontrivial weak solutions for fractional boundary value problems with variable coefficients[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(12): 45-51.

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