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一类分数阶Kirchhoff型方程非平凡解的存在性 被引量：4

Existence of a Nontrivial Solutions for a Class of Kirchhoff Nonlocal Operators of Elliptic Type
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摘要 利用临界点理论中的山路弓l理,研究一类分数阶Kirchhoff型方程在次临界增长条件下非平凡解的存在性,进一步统一和丰富了已有文献的相关结果. By using the mountain pass theorem in critical point theory, we study the existence of nontrivial solutions for a class of Kirchhoff nonlocal operators of elliptic type. The results improve and generalize some of the recent corresponding results.
作者 安育成
机构地区 毕节学院理学院
出处 《应用泛函分析学报》 CSCD 2014年第4期336-340,共5页 Acta Analysis Functionalis Applicata
基金 贵州省科学技术基金(黔科合J字LKB[2012]19号)
关键词 Kirchhoff型方程 非局部椭圆算子 山路引理 Kirchhoff type problems non-local elliptic operators mountain pass lemma
分类号 O176.3 [理学—基础数学] O177.91 [理学—基础数学]
  • 相关文献

参考文献12

  • 1Dipierro S,Pinamonti A.A geometric inequality and a symmetry result for elliptic systems involving the fractional Laplacian[J].Journal of Differential Equations,2013,255(1):85-119.
  • 2Bai C.Existence results for non-local operators of elliptic type[J].Nonlinear Analysis:Theory,Methods & Applications,2013,83:82-90.
  • 3Zhang Q G,Sun H R,Nieto J J.Positive solution for a superlinear Kirchhoff type problem with a parameter[J].Nonlinear Analysis:Theory,Methods & Applications,2014,95:333-338.
  • 4Chen C,Zhu Q.Existence of positive solutions to p-Kirchhoff-type problem without compactness conditions[J].Applied Mathematics Letters,2014,28:82-87.
  • 5Nyamoradi N.Existence of three solutions for Kirchhoff nonlocal operators of elliptic type[J].Mathematical Communications,2013,18(2):489-502.
  • 6Teng K.Two nontrivial solutions for hemivariational inequalities driven by nonlocal elliptic operators[J].Nonlinear Analysis:Real World Applications,2013,14(1):867-874.
  • 7Kajikiya R.Positive solutions of semilinear elliptic equations with small perturbations[J].Proceedings of the American Mathematical Society,2013,141(4):1335-1342.
  • 8Rasouli S H,Nategh M.Mountain pass solution to a class of nonlinear problems involving the p(x)-Laplacian operator[J].International Journal of Mathematics and StatisticsTM,2013,14(2):36-42.
  • 9Di Nezza E,Palatucci G,Valdinoci E.Hitchhiker's guide to the fractional Sobolev spaces[J].Bulletin des Sciences Mathématiques,2012,136:521-573.
  • 10Servadei R,Valdinoci E.The Brezis-Nirenberg result for the fractional Laplacian[J].Trans Amer Math Soc,http://www.math.utexas.edu/np-arc-bin/mpa?yn-11-196.

同被引文献14

引证文献4

二级引证文献5

应用泛函分析学报
2014年 第4期

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