The role of the boundary in some semilinear Neumann problems

Giovanni Mancini; Roberta Musina

Rendiconti del Seminario Matematico della Università di Padova (1992)

  • Volume: 88, page 127-138
  • ISSN: 0041-8994

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Mancini, Giovanni, and Musina, Roberta. "The role of the boundary in some semilinear Neumann problems." Rendiconti del Seminario Matematico della Università di Padova 88 (1992): 127-138. <http://eudml.org/doc/108263>.

@article{Mancini1992,
author = {Mancini, Giovanni, Musina, Roberta},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {semilinear Neumann problem; concentration compactness},
language = {eng},
pages = {127-138},
publisher = {Seminario Matematico of the University of Padua},
title = {The role of the boundary in some semilinear Neumann problems},
url = {http://eudml.org/doc/108263},
volume = {88},
year = {1992},
}

TY - JOUR
AU - Mancini, Giovanni
AU - Musina, Roberta
TI - The role of the boundary in some semilinear Neumann problems
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1992
PB - Seminario Matematico of the University of Padua
VL - 88
SP - 127
EP - 138
LA - eng
KW - semilinear Neumann problem; concentration compactness
UR - http://eudml.org/doc/108263
ER -

References

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  1. [1] Adimurthi - G. Mancini, The Neumann problem for elliptic equations with critical nonlinearity, Quaderni della Scuola Normale Superiore di Pisa, A, Volume in Honour of Giovanni Prodi (1991). Zbl0836.35048MR1205370
  2. [2] A. Bahri - J. M. CORON, On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain, Comm. Pure Appl. Math., 41 (1988), pp. 253-294. Zbl0649.35033MR929280
  3. [3] V. Benci - G. Cerami, The effect of the domain topology on the number of positive solutions, Arch. Rational Mech. Anal., to appear. Zbl0727.35055
  4. [4] V. Benci - G. Cerami - D. Passaseo, On the number of positive solutions of some nonlinear elliptic problems, Quaderni della Scuola Normale Superiore di Pisa, A, Volume in Honour of Giovanni Prodi (1991). Zbl0838.35040MR1205376
  5. [5] G. Cerami - D. Passaseo, Existence and multiplicity of positive solutions for nonlinear elliptic problems in exterior domains with «rich» topology, preprint. Zbl0810.35024MR1146601
  6. [6] J.M. Coron, Topologie et cas limite des injections de Sobolev, C.R. Acad. Sc. Paris, Ser. I Math., 299 (1984), pp. 209-212. Zbl0569.35032MR762722
  7. [7] E.N. Dancer, The effect of the domain shape on the number of positive solutions of certain nonlinear equations, J. Diff. Equations, 74 (1978), pp. 120-156. Zbl0662.34025MR949628
  8. [8] B. Gidas - W.M. Ni - L. Nirenberg, Symmetry of positive solutions of nonlinear elliptic equations RN, mathematical analysis and applications, Part A, Advances Mathematics Supplementary Studies, 7-AAcademic Press (1981), pp. 369-402. Zbl0469.35052
  9. [9] M. Grossi - F. Pacella, Positive solutions of nonlinear elliptic equations with critical Sobolev exponent and mixed boundary conditions, Proc. Royal Soc. Edinburgh, 116-A (1990), pp. 23-43. Zbl0724.35041MR1076352
  10. [10] J. Kazdan - F. WARNER, Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math., 28 (1975), pp. 567-597. Zbl0325.35038MR477445
  11. [11] M.K. Kwong, Uniqueness of positive solutions of Δu - u + up = 0, Arch. Rat. Mech. Anal., 105 (1989), pp. 243-266. Zbl0676.35032
  12. [12] P.L. Lions, The concentration-compactness principle in the calculus of variations: the locally compact case. Part. I, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1 (1984), pp. 109-145. Zbl0541.49009MR778970
  13. [13] P.L. Lions, The concentration-compactness principle in the calculus of variations: the locally compact case. Part. II, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1 (1984), pp. 223-283. Zbl0704.49004MR778974
  14. [14] W.M. Ni - I. Takagi, On the existence and the shape of solutions to a semilinear Neumann problem, preprint. Zbl0792.35057MR1167854

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