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A Semilinear Elliptic Equation with Double Resonance 被引量：1

A Semilinear Elliptic Equation with Double Resonance
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摘要 In this paper, the existence and multiplicity of a class of double resonant semilineax elliptic equations with the Dirichlet boundary value axe studied. In this paper, the existence and multiplicity of a class of double resonant semilineax elliptic equations with the Dirichlet boundary value axe studied.
作者 Mei Yue JIANG Ming Zheng SUN
机构地区 LMAM College of Sciences
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第7期1233-1246,共14页 数学学报（英文版）
基金 The first author is supported by -National Natural Science Foundation of China the second author is supported by the Doctoral Fund of North China University of Technology
关键词 Semilinear elliptic equation double resonance Semilinear elliptic equation, double resonance
分类号 O175.25 [理学—基础数学] TQ424.25 [化学工程]
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  • 1Amann, H., Zehnder, E.: Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci., 7, 539-603 (1980).
  • 2Chang, K.-C.: Infinite Dimensional Morse Theory and Multiple Solution Problems, Birkh~user, Boston, 1993.
  • 3Chang, K.-C.: Solutions of asymptotically linear operator via Morse theory. Comm. Pure Appl. Math., 34, 693-712 (1981).
  • 4Landesman, E. M., Lazer, A. C.: Nonlinear perturbations of linear eigenvalues problem at resonance. J. Math. Mech., 19, 609-623 (1970).
  • 5Landesman, E. M., Robinson, S., Rumbos, A.: Multiple solitions of semilinear elliptic problems at reso- nance. Nonlinear Anal., 24, 1049-1059 (1995).
  • 6Li, S.-J., Liu, J.-Q.: Computations of critical groups at degenerate critical point and application to nonlinear differential equations with resonance. Houston J. Ma~h., 25, 563-582 (1999).
  • 7Liu, Z.-L., Sun, J.-X.: An elliptic problem with jumping nonlinearities. Nonlinear Anal., 63, 1070-1082 (2005).
  • 8Su, J.-B.: Multiplicity results for asymptotically linear elliptic problems at resonance. J. Math. Anal. Appl., 27"8, 397-408 (2003).
  • 9Su, J.-B.: Existence and multiplicity results for classes of elliptic resonant problems. J. Math, Anal. Appl., 273, 565-579 (2002).
  • 10E1 Amrouss, A. R.: Multiplicity results for semilinear elliptic problems with resonance. Nonlinear Anal., 65, 634-646 (2006).

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Acta Mathematica Sinica,English Series
2011年 第7期

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