Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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MULTIPLICITY AND STABILITY OF SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS HAVING NOT NON-NEGATIVE MASS

  • Kim, Wan-Se (Department of Mathematics Hanyang University) ;
  • Ko, Bong-Soo (Department of Mathematics Education Cheju National University)
  • Published : 2000.01.01
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Abstract

In this paper, the multiplicity, stability and the structure of classical solutions of semilinear elliptic equations of the form (equation omitted) will be discussed. Here $\Omega$ is a smooth and bounded domain in $R^{n}$ (n $\geq$ 1), f(x,u) = │u│$^{\alpha}$/sgn(u)-h(x), 0 < $\alpha$ < 1, (n $\geq$ 1) and h is a ${\gamma}$- Holder continuous function on $\Omega$ for some 0 < ${\gamma}$ < 1.a}$ < 1.

Keywords

References

  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 On the existence of positive solutions for a class of semilinear elliptic boundary value problems K. Brown;H. Budin
  3. Infinite Dimensional Morse Theory and Mulitiple Solution Problems K. Chang
  4. J. Reine Angew. Math. v.371 Multiple fixed of positive mappings E. N. Dancer
  5. Nonlinear Analysis T.M.A. v.17 Upper and lower stability and index theory for positive mappings and applications
  6. On the stable solutions of quasilinear periodic-parabolic problems E. Dancer;P. Hess
  7. Nonlinear Analysis v.11 On the existence of multiple ordered solutions of nonlinear eigenvalue problems D. DeFigueiredo
  8. Nonlinear Functional Analysis K. Deimling
  9. Comm.Math. Phys. v.68 Symmetry and related properties via the maximum principle B. Gidas;W. Ni;L. Nirenberg
  10. Comm. Partial Differential Equations v.6 On multiple positive solutions of nonlinear elliptic equations P. Hess
  11. Nonlinear Analysis T.M.A. v.26 no.6 Existence of stable and unstable solutions for semilinear parabolic problems with a jumping nonlinearity N. Hirano;W. S. Kim
  12. Discrete and Continuous dynamical Systems v.2 no.2 Multiplicity and stability result for semilinear parabolic equations
  13. Comm. Partial Differential Equations v.4 Singularly perturbed semilinear elliptic boundary value problems F. Howes
  14. J. Differential Equations v.86 no.1 Semilinear elliptic singular pertubation problems with nonuniform interior behavior W. Kelley;B. Ko
  15. Comm. Appli. Anal. Multiplicity result for periodic solutions of semilinear parabolic W. S. Kim
  16. J. Math. Anal. Appli. v.231 Multiplicity result for semilinear dissipative hyperbolic equations
  17. J. Differential Equations v.101 no.1 The third solution of semilinear elliptic boundary value problems and applications to singular perturbation problems B. Ko
  18. Publ. Res. Inst. Math. Sci. v.15 Asymptotic behavior and stability of solutions of semilinear diffusion equations H. Matano
  19. Regional Conference Ser. Math. N40 Topological degree method in nonlinear boundary value problems J. Mawhin
  20. Results in Mathematics v.14 Landesman-Lazer type problems at an eigenvalue of odd multiplicity J. Mawhin;K. Schmitt
  21. Maximum Principles in Differential Equations M. Protter;H. Weinberger
  22. Trans. Amer. Math. Soc. v.272 Multiple critical points of perturbed symmetric functionals P. Rabinowitz
  23. Indiana Univ. Math. J. v.21 Monotone methods in nonlinear elliptic and parabolic equations D. Sattinger
  24. Nonlinear Analysis v.2 no.3 Boundary value problems for quasilinear second order elliptic equations K. Schmitt
  25. Variational Methods, applications ot nonlinear partial differential equations and Hamiltonian systems N. Struwe