On the Number of Solutions of Some Semilinear Elliptic Problems

Antonio Ambrosetti

Bollettino dell'Unione Matematica Italiana (2011)

  • Volume: 4, Issue: 3, page 313-319
  • ISSN: 0392-4041

Abstract

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We show that a class of semilinear boundary value problems possess exactly one positive solution and one negative solution.

How to cite

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Ambrosetti, Antonio. "On the Number of Solutions of Some Semilinear Elliptic Problems." Bollettino dell'Unione Matematica Italiana 4.3 (2011): 313-319. <http://eudml.org/doc/290726>.

@article{Ambrosetti2011,
abstract = {We show that a class of semilinear boundary value problems possess exactly one positive solution and one negative solution.},
author = {Ambrosetti, Antonio},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {313-319},
publisher = {Unione Matematica Italiana},
title = {On the Number of Solutions of Some Semilinear Elliptic Problems},
url = {http://eudml.org/doc/290726},
volume = {4},
year = {2011},
}

TY - JOUR
AU - Ambrosetti, Antonio
TI - On the Number of Solutions of Some Semilinear Elliptic Problems
JO - Bollettino dell'Unione Matematica Italiana
DA - 2011/10//
PB - Unione Matematica Italiana
VL - 4
IS - 3
SP - 313
EP - 319
AB - We show that a class of semilinear boundary value problems possess exactly one positive solution and one negative solution.
LA - eng
UR - http://eudml.org/doc/290726
ER -

References

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  1. AMBROSETTI, A. - MALCHIODI, A., Nonlinear analysis and semilinear elliptic problems, Cambridge Studies in Advanced Mathematics No. 104, Cambridge Univ. Press, 2006 Zbl1115.35004MR2292344DOI10.1017/CBO9780511618260
  2. AMBROSETTI, A. - MANCINI, G., Sharp nonuniqueness results for some nonlinear problems, J. Nonlin. Anal. TMA, 3-5 (1979), 635-645. MR541874DOI10.1016/0362-546X(79)90092-0
  3. AMBROSETTI, A. - PRODI, G., A Primer of Nonlinear Analysis, Cambridge Studies in Advanced Mathematics No. 34, Cambridge Univ. Press, 1993. Zbl0781.47046MR1225101
  4. AMBROSETTI, A. - PRODI, G., On the inversion of some differentiable appings with singularities between Banach spaces. Ann. Mat. Pura Appl., 93 (1972), 231-246. Zbl0288.35020MR320844DOI10.1007/BF02412022
  5. DE FIGUEIREDO, D. G., Lectures on Boundary Value Problems of Ambrosetti-Prodi Type, 12th Brazilian Seminar of Analysis, Sao Paulo, Brasil, 1980. 
  6. DE FIGUEIREDO, D. G., Positive solutions of semilinear elliptic problems, in Differential equations, Lecture Notes in Math.957Springer, 1982. Zbl0506.35038MR679140
  7. DE FIGUEIREDO, D. G. - GOSSEZ, J. P., Strict monotonicity of eigenvalues and Unique Continuation, Comm. P.D.E., 17-1 (1993), 339-346. MR1151266DOI10.1080/03605309208820844
  8. RUF, B., Singularity theory and the geometry of a nonlinear elliptic equation, Ann. Sc. Norm. Sup. Pisa, 17 (1990), 1-33. Zbl0725.35043MR1074625
  9. RUF, B., Forced secondary bifurcation in an elliptic boundary value problem, Diff. Int. Eq., 5-4 (1992), 793-804. Zbl0759.35010MR1167495

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