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Nonlinear Biharmonic Equations with Critical Potential 被引量：6

Nonlinear Biharmonic Equations with Critical Potential
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摘要 In this paper, we study two semilinear singular biharmonic equations： one with subcritical exponent and critical potential, another with sub-critical potential and critical exponent. By Pohozaev identity for singular solution, we prove there is no nontrivial solution for equations with critical exponent and critical potential. And by using the concentrate compactness principle and Mountain Pass theorem, respectively, we get two existence results for the two problems. Meanwhile, we have compared the changes of the critical dimensions in singular and non-singular cases, and we get an interesting result. In this paper, we study two semilinear singular biharmonic equations： one with subcritical exponent and critical potential, another with sub-critical potential and critical exponent. By Pohozaev identity for singular solution, we prove there is no nontrivial solution for equations with critical exponent and critical potential. And by using the concentrate compactness principle and Mountain Pass theorem, respectively, we get two existence results for the two problems. Meanwhile, we have compared the changes of the critical dimensions in singular and non-singular cases, and we get an interesting result.
作者 Hui XIONG Yao Tian SHEN
机构地区 Department of Applied Mathematics Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第6期1285-1294,共10页 数学学报（英文版）
基金 the National Natural Science Foundation of China (Nos.10171032,10071080,10101024)
关键词 Critical potential SINGULARITY Critical dimensions Disappear Critical potential, Singularity, Critical dimensions, Disappear
分类号 O175 [理学—基础数学]
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参考文献16

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同被引文献18

  • 1熊辉,沈尧天.半线性奇系数临界双调和方程的Dirichlet问题[J].数学物理学报（A辑）,2005,25(3):299-306. 被引量：8
  • 2邓义华,彭白玉.一类高阶边值问题正解的存在唯一性[J].江西师范大学学报（自然科学版）,2007,31(1):34-37. 被引量：2
  • 3Lions P L. The concentration-compactness principle in the calculus of varations: The locally compactcase[C]. Ann lnst H Poincare Anal Nonlineare, 1984, part 1: 109-145; part 2: 223-283.
  • 4Lions P L. The concentration-compactness principle in the calculus of varations: The limit case[C]. Rev Mat lberoamericano, 1985, part 1: 145-201; part 22: 45-121.
  • 5Chen Z C. The eigenvalue problem for p-Laplacian-like equations[J]. Acta Mathmeatics Sinica, 2003, 46(4):631 - 638.
  • 6Ghoussoub N, Yuan C. Multiple solutions for quasilinear PDES involving the critical Sobolev and Hardy exponents[J].Transactions of the American Mathematical Society, 2000,352(12): 5703-5743.
  • 7James W Dold, Victor A Galaktionov, Andrew A Lacey, et al. Rate of approach to a singular steady state in quasilinear reaction-diffusion equations [J] .Ann Scuola Noem Sup CI Sci, 1998,26(4) :663-687.
  • 8Hardy G H,Littlewood J E,Polya G. Inequalities [M] .2nd ed. Cambridge:Cambridge Univ Press, 1952.
  • 9Pucci P,Serrin J. Critical exponents and critical dimensions for polyharmonic equations [J] .J Math Pure Appl, 1990,69:55-83.
  • 10Edmunds D E, Fortunato D, Jannelli E. Critical exponents, critical dimensions and the biharmonic operator [ J ]. Arch Rational Mech Anal, 1990,112:269-289.

引证文献6

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Acta Mathematica Sinica,English Series
2005年 第6期

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