MULTIPLICITY RESULTS OF ORDERED POSITIVE SOLUTIONS FOR SEMILINEAR ELLIPTIC PROBLEMS ON Rn

  • Ko, Bong-Soo (Department of Mathematics Education Cheju National University) ;
  • Lee, Yong-Hoon (Department of Mathematics Pusan National University)
  • 발행 : 1999.03.01

초록

We prove the existence of 2N-1 distinct ordered positive solutions of a class of semilinear elliptic Dirichlet boundary value problems on Rn when the forcing term has N distinct positive stable zeros and the coefficient function decaying to the zero at infinity.

키워드

참고문헌

  1. SIAM Rev. v.18 no.4 Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces H. Amann
  2. SIAM J. Math. Anal. v.10 no.5 On the existence of positive solutions for a class of semilinear elliptic boundary value problems K. J. Brown;H. Budin
  3. Infinite dimensional Morse theory and multiple solution problems K. Chang
  4. J. Reine Angew. Math. v.371 Multiple fixed points of positive mappings E. Dancer
  5. Nonlinear Analysis v.11 no.4 On the exitence of multiple ordered solutions of nonlinear eigenvalue problems De Figueirdo
  6. J. Math. Anal. Appl. v.181 Upper and lawer solutions for a generalized Emden-Fowler equation P. Habets;F. Zanolin
  7. Comm. Partial Differential Equations v.6 no.8 On multiple positive solutions of nonlinear elliptic eigenvalue problems P. Hess
  8. J. Diff. Eqns. v.101 no.1 The third solution of semilinear elliptic boundary value problems and applications to singular perturbation problems B. Ko
  9. Int. and Diff. Eqns. Eigenvalues of singular boundary value problems and existence results for positive radial solutions of semilinear elliptic problems in exterior domains Y. H. Lee
  10. Indiana Univ. Math. J v.31 no.4 On the elliptic equation ${\Delta}u+K(x)u^\frac{n+2}{n-2}$=0, its generalizations, and applications in Geometry W. Ni