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由p(x)Laplace算子导出的不等式Dirichlet问题的三解

葛斌 薛小平 郭梦舒

葛斌, 薛小平, 郭梦舒. 由p(x)Laplace算子导出的不等式Dirichlet问题的三解[J]. 应用数学和力学, 2010, 31(10): 1220-1228. doi: 10.3879/j.issn.1000-0887.2010.10.009
引用本文: 葛斌, 薛小平, 郭梦舒. 由p(x)Laplace算子导出的不等式Dirichlet问题的三解[J]. 应用数学和力学, 2010, 31(10): 1220-1228. doi: 10.3879/j.issn.1000-0887.2010.10.009
GE Bin, XUE Xiao-ping, GUO Meng-shu. Three Solutions for Inequalities Dirichlet Problem Driven by p(x)-Laplacian[J]. Applied Mathematics and Mechanics, 2010, 31(10): 1220-1228. doi: 10.3879/j.issn.1000-0887.2010.10.009
Citation: GE Bin, XUE Xiao-ping, GUO Meng-shu. Three Solutions for Inequalities Dirichlet Problem Driven by p(x)-Laplacian[J]. Applied Mathematics and Mechanics, 2010, 31(10): 1220-1228. doi: 10.3879/j.issn.1000-0887.2010.10.009

由p(x)Laplace算子导出的不等式Dirichlet问题的三解

doi: 10.3879/j.issn.1000-0887.2010.10.009
基金项目: 国家自然科学基金资助项目(10971043;11001063);黑龙江省杰出青年基金资助项目(A200803)
详细信息
    作者简介:

    葛斌(1979- ),男,黑龙江人,讲师,博士(联系人.Tel:+86-451-55693902;E-mail:ge-bin791025@hrbeu.edu.cn);薛小平(1963- ),男,黑龙江人,教授,博士,博士生导师(E-mail:xiaopingxue@263.net);郭梦舒(1972- ),男,黑龙江人,副教授,博士(E-mail:msguo@hit.edu.cn).

  • 中图分类号: O175

Three Solutions for Inequalities Dirichlet Problem Driven by p(x)-Laplacian

  • 摘要: 讨论了一类具有非光滑位势的p(x)-Laplace非线性椭圆问题.利用非光滑的三临界点定理证明了该问题在变指数Sobolev空间W1,p(x)0(Ω)中至少存在3个非平凡解.
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    [2] Zhikov V V. Averaging of functionals of the calculus of variations and elasticity theory[J]. Math USSR Izv, 1987, 29(1):33-66. doi: 10.1070/IM1987v029n01ABEH000958
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    [4] Fan X L, Zhang Q H. Eigenvalues of p(x)-Laplacian Dirichlet problem[J]. J Math Anal Appl, 2005, 302(2):306-317. doi: 10.1016/j.jmaa.2003.11.020
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出版历程
  • 收稿日期:  1900-01-01
  • 修回日期:  2010-08-23
  • 刊出日期:  2010-10-15

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