대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제17권4호
  • /
  • Pages.565-576
  • /
  • 2002
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

Ambrosetti-Prodi형의 해의 다중존재문제

  • 김완세 (한양대학교 자연과학대학 수학과)
  • 발행 : 2002.10.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

본 개관에서는 Ambrosetti-Prodi형의 해의 다중존재성에 관하여 살펴볼 것이다.

키워드

참고문헌

  1. Proc. R. Soc. Edinb v.84A A Multiplicity result for a class of elliptic boundary valve problems H. Amann;P. Hess
  2. Ann, Mat. Pura. Appl v.93 On the inversion of some differential mappings with singularities between Banach space A. Ambrosetti;G. Prodi
  3. J. Diff. Eq v.13 Periodic boundary value problems for system of second order differential equations J.W. Bebernes;K. Schmitt https://doi.org/10.1016/0022-0396(73)90030-2
  4. Bo. Soc. Brasil. Mat v.12 Sharp existence results for a class of semilinear elliptic problems H. Berestycki;P.L. Lions https://doi.org/10.1007/BF02588317
  5. Math. J. v.24 On the solution of a nonlinear Dirichlet problem M.S. Berger;E. Podolak
  6. Semin. Math. U.C.L. (NS) no.79 Finiteness of the set of solutions of some boundary value problems for ordinary differential equations L. Brull;J. mawhin
  7. Ssinetia Sinicqa A-26 Variational methods and sub-and super-solutions K.C. Chang
  8. J. Diff. Eq v.69 no.3 Generalized Ambrosetti-Prodi condi-tions for nonlinear two-point boundary value problems R. Chiapiiinelli;J. Mawhin;R. Nugari https://doi.org/10.1016/0022-0396(87)90127-6
  9. J. math. Pures Appl. v.57 On the range of certain weakly nonlinear elliptic partial differential equations E.N. Dancer
  10. J. Reine Angew. Math v.350 Degenerate critical points, homotopy indices, and Morse inequalities
  11. Atas do 12° Seminario Brasileiro de Analise, Sao Paulo Lecture on boundary value problems of the Ambrosetti Prodi type
  12. J. Nonlin. Anal v.8 On the superlinear Ambrosetti-prodi problem https://doi.org/10.1016/0362-546X(84)90010-5
  13. Comm. Partial Differential Equations v.9 Variational approach to superlinear elliptic problems D.G. De Figueiredo;S. Solomini https://doi.org/10.1080/03605308408820345
  14. Diff. Int. Eq v.1 no.1 A multiplicity result for periodic solutions of higher order ordernary differential equations S.H. Ding;J. Mawhin
  15. Mono-grapi 41/42 Erzwungene Schwingungen bei veranderlicher Eigenfrequenz G. Duffing
  16. Bull. London Math. Soc v.18 A multiplicity result for periodic solutions of forced nonlinear second order ordinary differential equations C. Fabry;J. Mawhin;M.N. Nkashama https://doi.org/10.1112/blms/18.2.173
  17. J. of Diff. Eq v.18 On periodic solutions of forced pendulum-like equa-tions G. Fourier;J. Mawhin
  18. Boll. Un. Mat. Ital. v.II Remark on a result S. Fucik;A. Ambrosetti;G. Prodi
  19. Springer Lecture Notes in Mathematics v.568 Coincidence drgree and nonlinear differential equa-tions R.E. Gaines;J. Mawhin
  20. SIAM J. Math. Anal v.17 no.6 Multiplicity of solutions of nonlinear boundary valve problems D.C. Hart;A.C. Lazer;P.J. Mckenna https://doi.org/10.1137/0517093
  21. Differential and Integral Eq v.8 no.7 Multiple existense of periodic solutions for Lienard system N. Hirano;W.S. Kim
  22. Nonlinear Analysis T.M.A. v.26 no.6 Existence of stable and unstable solutions for semilinear parabolic prob-lems with a jumping nonlinearity https://doi.org/10.1016/0362-546X(94)00284-O
  23. Dis-crete and Continuous Dynamical System v.2 no.2 Multiplicity and stability result for semilinear parabolic equations https://doi.org/10.3934/dcds.1996.2.271
  24. Multiple existence of periodic solutions for a nonlinear parabolic problem with singular nonlinearities https://doi.org/10.1016/S0362-546X(03)00101-9
  25. Math. Ann v.261 variational and topological methods in partially ordered banach space H. Hofer https://doi.org/10.1007/BF01457453
  26. Proc. Roy. Soc. Edin v.110A Periodic solutions of forced Lienard equations with jumping nonlinearities under nonuniform condi-tions R. Iannacci;M.N. Nkashama;P. Omari;F. Zanolin
  27. Czechoslovak Math J. v.37 no.112;3 Superlinear elliptic boundary value problems R. Kannan;R. Ortega
  28. Comm. Appl. Math. v.28 Remarks on some qusilinear elliptic equations J.L. Kazan;F.W. Warner https://doi.org/10.1002/cpa.3160280502
  29. Inter. J. Math. Math., Sci. v.18 no.2 Existence of periodic solutions for nonlinear Lienard system W.S. Kim https://doi.org/10.1155/S0161171295000329
  30. J. Math. Anal. Appl v.197 Multiple doubly periodic solutions of semilinear dissipative hyperbolic equations https://doi.org/10.1006/jmaa.1996.0049
  31. Appl. Anal v.6 no.1 Multiplicity result for periodic solutions of semilinear parabolic equ-tions
  32. Huston J. Math Multiple existence of periodic solutions for semilinear parabolic equations with small nonlinear term
  33. Multiple existence of periodic solutions for semilinear parbolic equations with small nonlinear term
  34. Lecture Note in Math v.1324 Introduction to multiplicity theory for boundary value problems with asymetric nonlinearities A.C. Lazer https://doi.org/10.1007/BFb0100789
  35. J. Math. Anal. Appl v.84 On the number of solutions of a nonlinear Dirich-let problem A.C. Lazerand;P.J. McKenna https://doi.org/10.1016/0022-247X(81)90166-9
  36. Proc. Roy. Soc. Edinburgh Sect. v.A95 no.3;4 On a conjecture related to the number of a nonlinear Dirchlet problem
  37. J. Math. Anal. Appl v.107 no.2 Multiplicity results for a class of semilinear elliptic and parabolic bound-ary value problems
  38. Nonlinear Analysis T.M.A. v.9 no.4 Multiplicity results for a semilinear boundary value problem with the nonlinearity crossing higher eigenvalues https://doi.org/10.1016/0362-546X(85)90058-6
  39. Commu. PDE v.10 no.2 Critical point theory and boundary value problems with nonlinearities crossing multiple eigenvalues https://doi.org/10.1080/03605308508820374
  40. J. Reine Angew. Math v.368 Multiplicity of solutions of nonlinear boundary value problems with non-linearities crossing several higher eigenvalues
  41. Doctorial Thesis Ambrosetti-Prodi type results for periodic solutions of second-order ordirnary differential system Y.H. Lee
  42. Sem. Math. Sup no.92 Pooints fixes, points critiques et a problemes aux limites J. Mawhin
  43. Proc. International Conference v.1285 Ambrosetti-Prodi type result in nonlinear boundary value problems https://doi.org/10.1007/BFb0080609
  44. Z. Angew. Math. Phys. v.38 First order ordinary differential equations with several periodic solutions https://doi.org/10.1007/BF00945410
  45. Lecture Note Math v.964 Periodic oscillations of forced pendulum-like equations https://doi.org/10.1007/BFb0065017
  46. Rocky Mountain J. Math v.12 Nonuniform resonance conditions at the two first eigenvalues for periodic solutions of forced Lienard and Duffing equations J. Mawhin;J.R. Ward https://doi.org/10.1216/RMJ-1982-12-4-643
  47. Arch. Math (Basel) v.41 Periodic solutions of some forced Lienard differential equations at reso-nance https://doi.org/10.1007/BF01371406
  48. J. Diff. Eq v.52 Multiple solutions of the periodic boundary value problem for nonlinear first order ordinary differential equations J. Mawhin;M. Willem https://doi.org/10.1016/0022-0396(84)90180-3
  49. J. Math. Anal. Appl. v.140 A generalized upper and lower solutions methods and multi-plicity results for nonlinear first order ordinary differential equations M.N. Nakashama https://doi.org/10.1016/0022-247X(89)90072-3
  50. Ph. D. Thesis, Louvain-la Neuve Conditions de resonance ou de non-resonance non-uniforms et solu-tions periodique d, equations fifferentielles non lineaires
  51. Boll. U.M.I. v.3-B no.7 Stability and index of periodic solutions of an equation of Duffing type R. Ortega
  52. Diff. Int. Eq v.1;2 Multiple periodic solutions for some nonlinear ordi-nary differential equations of higher order M. Ramos;L. Sanchez
  53. Masson et Cie v.VI E'quations Differ'entielles Ordinaires I,II N. et Rauch;J. Mawhin
  54. nonlinear Analysis T.M.A. v.7 Existence of a third solutions for a class of boundary value problems with jumping nonlinearities S. Solimini https://doi.org/10.1016/0362-546X(83)90067-6
  55. J. Nonlinear Anal v.6 pertubations with some superlinear growth for a class of second order elliptic boundary value problems J.R. Ward https://doi.org/10.1016/0362-546X(82)90022-0