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一类含p(x)-Laplace算子的拟线性椭圆方程三解的存在性 被引量：1

Three Solutions for A Class of Quasilinear Elliptic Equations Involving the p(x)-Laplace Operator
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摘要 讨论了一类含p(x)-Laplace算子的拟线性椭圆方程.在Dirichlet边界条件下解的存在性,利用B.Ricceri的三解定理得到了方程至少存在三个弱解. The existence of at least three weak solutions is established for a class of quasilinear elliptic equations involving the p （x）-Laplace operator with Dirichlet boundary condition. The technical approach is mainly baced on a three critical points theorem due to Riceeri.
作者 尹洪辉 刘英
机构地区 淮阴师范学院数学科学学院
出处 《淮阴师范学院学报（自然科学版）》 CAS 2012年第2期111-116,共6页 Journal of Huaiyin Teachers College;Natural Science Edition
关键词 p(x)-Laplace算子 SOBOLEV空间 三解定理 p（x）-Laplacian Sobolev space three critical points theorem
分类号 O175.8 [理学—基础数学]
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参考文献13

  • 1Anello G, Cordaro G. Existence of solutions of the Neumann problem for a class of equations involving the p-Laplacian via avaria- tional principle of Ricceri [ J]. Arch Math, 2002,79 : 274 - 287.
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同被引文献16

  • 1Yin H H,Wen J.Three solutions for a class of quasilinear elliptic equation involving the p-q-Laplace operator[J].Math Meth Appl Sci,2014,37(3):428-434.
  • 2Ricceri B.A three critical points theorem revisited[J].Nonlinear Anal,2009,70(9):3084-3089.
  • 3Ruzicka M.Electro-rheological Fluids:Modeling and Mathematical Theory,Lecture Notes in Math[M].Springer-Verlag,Berlin,2000.
  • 4Zhikov V V.Averaging of functionals of the calculus of variations and elasticity theory[J].Math Ussr Izv,1987,29(1):33-36.
  • 5Ricceri B.On three critical points theorem[J].Arch Math,2000,75(2):220-226.
  • 6Mihailescu M.Existence and multiplicity of solutions for a Neumann problem imvolving the p(x)-Laplaceoperator[J].Nonlinear Anal,2007,67(5):1419-1425.
  • 7Shi X Y,Ding X H.Existence and multiplicity of solutions for a general p(x)-Laplacian Neumann problem[J].Nonlinear Anal,2009,70(10):3715-3720.
  • 8Yin H H.Existence of three solutions for a Neumann problem involving the p(x)-Laplace operator[J].Math Meth Appl Sci,2012,35(3):307-313.
  • 9Bonanno G,Candito P.Three solutions to a Neumann problem for elliptic equations involving the p-Laplacian[J].Arch Math,2003,80(4):424-429.
  • 10Bonanno G.A minimax inequality and its applications to ordinary differential equations[J].J Math Anal Appl,2002,270(1):210-219.

引证文献1

淮阴师范学院学报（自然科学版）
2012年 第2期

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