Publication Cover
Applicable Analysis
An International Journal
Volume 56, 1995 - Issue 3-4
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Original Articles

On sign-changing solutions of certain semilinear elliptic problems

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Pages 193-206 | Received 25 Feb 1994, Published online: 20 Jan 2011

References

  • Amann , H. 1976 . Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces . SIAM Review , 18 : 620 – 709 .
  • d'Aujourdlhui M. Sur l'ensemble de resonance d'un problem demi- lineaire preprint, Ecole Polytechnique de Lausanne.
  • Brezis , H. and Turner , R.E.L. 1977 . On a class of supperlinear elliptic problems . Comm. Part. Diff. Eqns. , 2 : 601 – 604 .
  • Chang , K.C. 1985 . Infinite Dimensional Morse Theory and Its Applications , Montreal : Univ. de .
  • Dancer , E.N. 1977 . On the Dirichlet problem for weakly nonlinear elliptic partial differential equations . Proc. Royal Soc. Edinburgh , 76A : 283 – 300 .
  • Dancer , E.N. 1984 . Degenerate critical points, homotopy indices and Morse inequalities . J. Reine Angew. Math. , 350 : 1 – 22 .
  • Dancer , E.N. 1991 . Upper and lower stability and index theory for positive mappings and applications . Nonlinear Analysis TMA , 17 : 205 – 217 .
  • Dancer , E.N. 1990 . The effect of domain shape on the number of positive solutions of certain nonlinear equations 11 . J. Diff. Eqns. , 87 : 316 – 339 .
  • Dancer , E.N. 1986 . Multiple fixed points of positive mappings . J. Reine Angew. Math. , 271 : 46 – 66 .
  • Dancer , E.N. and Du , Y. Competing species equations with diffusion, large interactions and jumping nonlinearities . to appear in J. Diff. Eqns. ,
  • Dancer , E.N. and Dul , Y. “ Existence of changing sign solutions for some semilinear problems with juiping nonlinearities at zero ” . Edinburgh . to appear in Proc. Royal Soc.
  • Dancer , E.N. and Du , Y. Multiple solutions of some semilinear elliptic equations via the generalized Conley index . to appear in J. Math. Anal. Appl ,
  • Dancer , E.N. and Guo , Z.M. Uniqueness and stability for solutions of competing species equations with large inteactions . to appear in Comm. Applied Nonlinear Analysis. ,
  • Deimling , K. 1985 . Nonlinear Functional Analysis , Berlin : Springer-Verlag .
  • de Figueiredo , D.G. , Lions , P.L. and Nussbaum , R.D. 1982 . A priori estimates and existence of positive solutions of semilinear elliptic equations . J. Math. Pures et Appl. , 61 : 41 – 63 .
  • Fucik , S. 1976 . Boundary value problems with jumping nonlinearities . Casopis Pest. Mat. , 101 : 69 – 87 .
  • Gidas , B. and Spruck , J. 1981 . A priori bounds for positive solutions of nonlinear elliptic equations . Comm. Part. Diff. Eqns. , 6 : 883 – 901 .
  • Gilbarg , D. and Trudinger , N. 1977 . Elliptic Partial Differential Equations of Second Order , Berlin : Springer .
  • Hofer , H. 1984 . A note on the topological degree of a critical point of mountain pass type . Proc. Amer. Math. Soc. , 90 : 309 – 315 .
  • Hofer , H. 1982 . Variational and topological methods in partially ordered Hilbert spaces . Math. Ann. , 261 : 493 – 514 .
  • Krasnoselskii , M.A. 1964 . Positive solutions of Operator Equations . Noordhoff , Groningen
  • Nussbaum , R.D. 1971 . The fixed point index for locally condensing maps . Ann. Mat. Pura. Appl. , 87 : 217 – 258 .
  • Rabinowitz , P.H. 1986 . Minimax Methods in Critical Point Theory with Applications to Differential Equations . CBMS Ser. in Math. , 65 AMS, Providence
  • Sweers , G. 1992 . “ A sign-changing global minimizer on a convex domain ” . In Progress in Partial Differential Equations , Edited by: Bandle , C. 251 – 258 . Pitman .
  • Wang , Z.Q. 1991 . On a superlinear elliptic equation Analyse Nonlineaire . Ann. Inst. Henri Poincare , 8 : 43 – 5 .

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