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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (8): 95-102.doi: 10.6040/j.issn.1671-9352.0.2021.220

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具有变号权函数的分数阶p-q-Laplacian方程组的多重解

李春平,桑彦彬*   

  1. 中北大学理学院, 山西 太原 030051
  • 出版日期:2022-08-20 发布日期:2022-06-29
  • 作者简介:李春平(1994— ),女, 硕士研究生, 研究方向为非线性微分方程. E-mail:952984231@qq.com*通信作者简介:桑彦彬(1979— ),男, 博士, 副教授, 硕士生导师, 研究方向为非线性微分方程. E-mail:sangyanbin@126.com
  • 基金资助:
    山西省高等学校科技创新计划资助项目(201802085);山西省基础研究计划资助项目(202103021224198)

Multiple solutions of fractional p-q-Laplacian system with sign-changing weight functions

LI Chun-ping, SANG Yan-bin*   

  1. School of Science, North University of China, Taiyuan 030051, Shanxi, China
  • Online:2022-08-20 Published:2022-06-29

摘要: 考虑一类具有凹凸非线性项和变号权函数的分数阶p-q-Laplacian方程组,借助于Nehari流形和Ekeland变分原理,证明当参数(λ, μ)属于Rn的某个集合时,该方程组至少存在两个非平凡解。

关键词: 变号权函数, Nehari流形, Ekeland变分原理, p-q-Laplacian

Abstract: The multiple solutions of fractional p-q-Laplacian system involving concave-convex nonlinearities and sign-changing weight functions is considered. The system has at least two nontrivial solutions when the pair of the parameters(λ, μ)belongs to a certain subset of Rn are proved by making use of the Nehari manifold and Ekelands variational principle.

Key words: sign-changing weight functions, Nehari manifold, Ekelands variational principle, p-q-Laplacian

中图分类号: 

  • O175.8
[1] ZHEN Maoding, HE Jinchun, XU Haoyun. Critical system involving fractional Laplacian[J]. Communications on Pure and Applied Analysis, 2019, 18(1):237-253.
[2] LEHRER R, MAIA L A, SQUASSINA M. On fractional p-Laplacian problems with weight [J]. Differential Integral Equations, 2015, 28(1/2):15-28.
[3] ZHEN Maoding, HE Jinchun, XU Haoyun, et al. Positive ground state solutions for fractional Laplacian system with one critical exponent and one subcritical exponent[J]. Discrete and Continuous Dynamical Systems, 2019, 39(11):6523-6539.
[4] PUCCI P, XIANG M Q, ZHANG B L. Multiple solutions for nonhomogeneous Schrödinger-Kirchhoff type equations involving the fractional p-Laplacian in Rn[J]. Calculus of Variations and Partial Differential Equations, 2015, 54(3):2785-2806.
[5] 顾秋婷, 沈自飞. 带变号势函数的分数阶p-Laplacian方程弱解的存在性[J]. 浙江师范大学学报(自然科学版), 2018, 41(1):12-18. GU Qiuting, SHEN Zifei. Existence of weak solutions for a fractional p-Laplacian equation with sign-changing potential[J]. Journal of Zhejiang Normal University(Natural Sciences), 2018, 41(1):12-18.
[6] GOYAL S, SREENADH K. Existence of multiple solutions of p-fractional Laplace operator with sign-changing weight function[J]. Advances in Nonlinear Analysis, 2015, 4(1):37-58.
[7] PERERA K, SQUASSINA M, YANG Y. A note on the Dancer-Fucik spectra of the fractional p-Laplacian and Laplacian operators[J]. Advances in Nonlinear Analysis, 2014, 4(1):13-23.
[8] XIANG M Q, ZHANG B L, RADULESCU V. Superlinear Schrödinger-Kirchhoff type problems involving the fractional p-Laplacian and critical exponent[J]. Advances in Nonlinear Analysis, 2020, 9(1):690-709.
[9] 张金国, 焦红英, 刘邱云. 分数阶p(x)-Laplace算子方程的多解性[J]. 数学杂志, 2020, 40(1):81-89. ZHANG Jinguo, JIAO Hongying, LIU Qiuyun. Multiplicity of solutions for fractional p(x)-Laplace equation[J]. Journal of Mathematics, 2020, 40(1):81-89.
[10] SERVADEI R, VALDINOCI E.Variational methods for non-local operators of elliptic type[J]. Discrete and Continuous Dynamical Systems, 2013, 33(5):2105-2137.
[11] ZHEN Maoding, ZHANG Binlin. The Nehari manifold for fractional p-Laplacian system involving concave-convex nonlinearities and sign-changing weight functions[J]. Complex Variables and Elliptic Equations, 2021, 66(10):1731-1754.
[12] CHEN Wenjing, DENG Shengbing. The Nehari manifold for a fractional p-Laplacian system involving concave-convex nonlinearities[J]. Nonlinear Analysis Real World Applications, 2016, 27:80-92.
[13] HE X, SQUASSINA M, ZOU W. The Nehari manifold for fractional systems involving critical nonlin-earrities[J]. Communications on Pure and Applied Analysis, 2016, 15(4):1285-1308.
[14] 李瑞. 一类非局部p-q-Laplace方程非负解的存在性[J]. 郑州大学学报(理学版), 2016, 48(2):5-10. LI Rui. Existence of nonnegative solution to a class of p-q-Laplace Equation[J]. Journal of Zhengzhou University(Natural Science), 2016, 48(2):5-10.
[15] 徐冬, 邓志颖. 含Hardy-Sobolev临界指数项的p-q型椭圆边值问题的非平凡解[J]. 应用数学, 2018, 31(2):269-280. XU Dong, DENG Zhiying. On nontrivial solutions of p-q Laplacian type elliptic boundary value problems involving Hardy-Sobolev critical exponents[J]. Mathematica Applicata, 2018, 31(2):269-280.
[16] XIANG M, ZHANG B, FERRARA M. Existence of solutions for Kirchhoff type problem involving thenon-local fractional p-Laplacian[J]. Journal of Mathematical Analysis and Applications, 2015, 424(2):1021-1041.
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