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一类边值问题的正解个数

Exact Number of Positive Solutions for a Class of Boundary Value Problems
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摘要 讨论了边值问题(｜y′｜p-2y′)′+λ(yα+yβ)=0,y(-1)=y(1)=0的正解存在性.其主要结论是:若p>1,β>p-1>α>-1+β+4βp2+p(2+3β+5p)1+β+4βp2+p(3+4β+4p),则存在λ>0使得当0<λ<λ时此边值问题恰好存在两个正解,当λ=λ时存在唯一正解,当λ>λ时不存在正解. We consider the boundary value problem:(｜y′｜ p-2 y′)′+λ(yα+yβ)=0 , y(-1)=y(1)=0.The main result is as follows:if p>1 andβ>p-1>α>-1+β+4βp2+p(2+3β+5p)1+β+4βp2+p(3+4β+4p),then there exists λ*>0 such that the problem has exactly two positive solutions for 0<λ<λ*,exactly one for λ=λ*,and none for λ>λ*.
作者 董安广 刘建勇 程建纲
机构地区 烟台师范学院交通学院 烟台大学数学与信息科学系
出处 《烟台大学学报（自然科学与工程版）》 CAS 2005年第2期91-97,共7页 Journal of Yantai University(Natural Science and Engineering Edition)
基金 国家自然科学基金资助项目(10251002) 山东省自然科学基金资助项目(Y2002A10)
关键词 边值问题 正解 存在性 boundary value problems positive solutions existence
分类号 O175.8 [理学—基础数学]
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参考文献13

  • 1Cheng Y.On an open problem of Ambrosetti,Brezis and Cerami[J].Differential Integral Equations,2002,15:1025～1044.
  • 2Liu Z.Exact number of solutions of a class of two-point boundary value problems involving concave and convex nonlinearities[J].Nonlinear Anal,2001,46:181～197.
  • 3程建纲.一类两点边值问题的正解个数[J].数学年刊（A辑）,2004,25(3):279-284. 被引量：8
  • 4韦忠礼,庞常词.一类含有p-Laplacian算子的奇异边值问题解的确切个数[J].数学年刊（A辑）,2004,25(2):207-216. 被引量：5
  • 5Addou I.Multiplicity of solutions for quasilinear elliptic boundary-value problems[J].Electron J Differential Equations,1999,21:1～27.
  • 6Addou I,Wang S.Exact multiplicity results for a p-Laplacian problem with concave-convex-concave nonlinearities[J].Nonlinear Anal,2003,53:111～137.
  • 7Castro A,Gadam S,Shivaji R.Evolution of positive solution curves in semiposition problems with concave nonlinearities[J].J Math Anal Appl,2000,245:282～293.
  • 8Cheng J.Exact number of positive solutions for a class of semiposition problems[J].J Math Anal Appl,2003,280:197～208.
  • 9Karatson I,Simon P L.Exact multiplicity for degenerate two-point boundary value problems with p-convex nonlinearity[J].Nonlinear Anal,2003,52:1569～1590.
  • 10Sanchez J,Ubilla P.Uniqueness results for the one-dimensional m-Laplacian considering superlinear nonlinearities[J].Nonlinear Anal,2003,54:927～938.

二级参考文献21

  • 1Agarwal,R.P.&amp; O'Regan,D.,Singular boundary value problems for superlinear secondorder ordinary and delay differential equations [J],J.Differential Equations,130(1996),333-355.
  • 2Lions,P.L.,On the existence of positive solutions of semilinear elliptice equations [J],SIAM Rev.,24(1982),441-467.
  • 3Wang Shinhwa &amp; Long Dauming,An exact multiplicity theorem involving concaveconvex nonlinearities and its application to statinary solutions of a singular diffusionproblem [J],Nonlinear Analysis T.M.A.,44(2001),469-486.
  • 4Korman,P.,Li,Y.&amp; Ouyang,T.,Exact multiplicity results for boundary value problemswith nonlinearities generalising cubic [J],Proc.Roy.Soc.Edinburgh,126A(1996),599-616.
  • 5Korman,P.&amp; Ouyang,T.,Exact multiplicity results for two classes of boundary valueproblems [J],Differential Integral Equations,6(1993),1507-1517.
  • 6Laetsch,T.,The number of solutions of a nonlinear two Point boundary value problem[J],Indiana Univ.Math.J.,20(1970),1-13.
  • 7Smoller,J.&amp; Wasserman,A.,Global bifurcation of steady-state solutions [J],J.Differential Equations,39(1981),269 290.
  • 8Korman,P.&amp; Ouyang,T.,Multiplicity results for two classes of boundary value problems [J],SIAM J.Math.Anal.,26(1995),180-189.
  • 9Zhang,L.,Uniqueness of positive solutions of △u + u + up = 0 in a ball [J],Comm.Partial Equations,7(1992),1141 1164.
  • 10Zhang,L.,Uniqueness of positive solutions of semilinear elliptic equations [J],J.Differential Equations,115(1995),1-23.

共引文献10

烟台大学学报（自然科学与工程版）
2005年 第2期

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