Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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EXISTENCE OF THE THIRD POSITIVE RADIAL SOLUTION OF A SEMILINEAR ELLIPTIC PROBLEM ON AN UNBOUNDED DOMAIN

  • Ko, Bong-Soo (Department of Mathematics Education, Cheju National University) ;
  • Lee, Yong-Hoon (Department of Mathematics Education, Cheju National University)
  • Published : 2002.05.01
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Abstract

We prove the multiplicity of ordered positive radial solutions for a semilinear elliptic problem defined on an exterior domain. The key argument is to prove the existence of the third solution in presence of two known solutions. For this, we obtain some partial results related to three solutions theorem for certain singular boundary value problems. Proof are mainly based on the upper and lower solutions method and degree theory.

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References

  1. SIAM Rev. v.18 no.4 Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces H. Amann
  2. Researches de mathematique 46 On the existence and multiplicity of positive solutions of the p-Laplacian separated boundary value problem A. Ben-Naoum;C. De Coster
  3. SIMA J. Math. Anal. v.10 no.5 On the existence of positive solutions for a class of semilinear elliptic boundary value problems K. J. Browm;H. Budin https://doi.org/10.1137/0510082
  4. Infinite dimensional Morse theory and multiple solution problems K. Chang
  5. Nonlinear Anal. v.27 no.6 Positive solutions of singular boundary value problems R. Dalmasso https://doi.org/10.1016/0362-546X(95)00073-5
  6. J. Reine Angew. Math. v.371 Multiple fixed points of positive mappings E. Dancer
  7. Nonlinear Anal. v.11 no.4 On the existence of multiple ordered solutions of nonlinear eigenvalue problems De Figueirdo https://doi.org/10.1016/0362-546X(87)90066-6
  8. Nonlinear Anal. v.28 no.8 Existence of multiple positive solutions of singular boundary value problems K. Ha;Y. Lee https://doi.org/10.1016/0362-546X(95)00231-J
  9. J. Math. Anal. Appl. v.181 Upper and lower solutions for a generalized Endem-Fowler equation P. Habets;F. Zanolin https://doi.org/10.1006/jmaa.1994.1052
  10. Comm. Partial Differential Equations v.6 no.8 On multiple positive solutions of nonlinear elliptic eigenvalue problems P. Hess https://doi.org/10.1080/03605308108820200
  11. J. Differential Equations v.101 no.1 The third solution of semilinear elliptic boundary value problems and applications to singular perturbation problems B. Ko https://doi.org/10.1006/jdeq.1993.1001
  12. SIAM J. Appl. Math. v.26 no.4 Solutions of a differential equation arising in chemical reactor processes S. Parter https://doi.org/10.1137/0126063
  13. Maximum Principles in Differential Equations M. Protter;H. Weinberger

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