On a semilinear elliptic eigenvalue problem

Mario Michele Coclite

Annales Polonici Mathematici (1997)

  • Volume: 67, Issue: 3, page 289-295
  • ISSN: 0066-2216

Abstract

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We obtain a description of the spectrum and estimates for generalized positive solutions of -Δu = λ(f(x) + h(u)) in Ω, u | ∂ Ω = 0 , where f(x) and h(u) satisfy minimal regularity assumptions.

How to cite

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Mario Michele Coclite. "On a semilinear elliptic eigenvalue problem." Annales Polonici Mathematici 67.3 (1997): 289-295. <http://eudml.org/doc/270431>.

@article{MarioMicheleCoclite1997,
abstract = {We obtain a description of the spectrum and estimates for generalized positive solutions of -Δu = λ(f(x) + h(u)) in Ω, $u|_\{∂Ω\} = 0$, where f(x) and h(u) satisfy minimal regularity assumptions.},
author = {Mario Michele Coclite},
journal = {Annales Polonici Mathematici},
keywords = {semilinear elliptic equations; nonlinear boundary-value problems; positive solutions; supersolution and subsolution method},
language = {eng},
number = {3},
pages = {289-295},
title = {On a semilinear elliptic eigenvalue problem},
url = {http://eudml.org/doc/270431},
volume = {67},
year = {1997},
}

TY - JOUR
AU - Mario Michele Coclite
TI - On a semilinear elliptic eigenvalue problem
JO - Annales Polonici Mathematici
PY - 1997
VL - 67
IS - 3
SP - 289
EP - 295
AB - We obtain a description of the spectrum and estimates for generalized positive solutions of -Δu = λ(f(x) + h(u)) in Ω, $u|_{∂Ω} = 0$, where f(x) and h(u) satisfy minimal regularity assumptions.
LA - eng
KW - semilinear elliptic equations; nonlinear boundary-value problems; positive solutions; supersolution and subsolution method
UR - http://eudml.org/doc/270431
ER -

References

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  1. [1] A. Ambrosetti, A perturbation theorem for superlinear boundary value problems, Math. Res. Center, Univ. of Wisconsin-Madison, Tech. Sum. Report #1446 (1974). 
  2. [2] A. Bahri and H. Berestycki, A perturbation method in critical point theory and applications, Trans. Amer. Math. Soc. 267 (1981), 1-32. Zbl0476.35030
  3. [3] G. Bonanno, Semilinear elliptic eigenvalue problems, preprint, 1995. 
  4. [4] G. Bonanno and S. A. Marano, Positive solutions of elliptic equations with discontinuous nonlinearities, Topol. Methods Nonlinear Anal. 8 (1996), 263-273. Zbl0891.35038
  5. [5] J. M. Bony, Principe du maximum dans les espaces de Sobolev, C. R. Acad. Sci. Paris Sér. A 265 (1967), 333-336. Zbl0164.16803
  6. [6] H. Brezis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), 437-477. 
  7. [7] K. J. Brown and H. Budin, Multiple positive solutions for a class of nonlinear boundary value problems, J. Math. Anal. Appl. 60 (1977), 329-338. Zbl0361.35023
  8. [8] M. M. Coclite, On a singular nonlinear Dirichlet problem. II, Boll. Un. Mat. Ital. B (7) 5 (1991), 955-975. Zbl0789.35057
  9. [9] M. M. Coclite, On a singular nonlinear Dirichlet problem. III, Nonlinear Anal. 21 (1993), 547-564. Zbl0799.35076
  10. [10] M. M. Coclite, On a singular nonlinear Dirichlet problem. IV, Nonlinear Anal. 23 (1994), 925-936. Zbl0814.35035
  11. [11] M. G. Crandall and P. H. Rabinowitz, Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems, Arch. Rational Mech. Anal. 58 (1975), 207-218. Zbl0309.35057
  12. [12] S. Gomes, On a singular nonlinear elliptic problem, SIAM J. Math. Anal. 17 (1986), 1359-1369. Zbl0614.35037
  13. [13] J. P. Keener and H. B. Keller, Positive solutions of convex nonlinear eigenvalue problems, J. Differential Equations 16 (1974), 103-125. Zbl0287.35074
  14. [14] H. B. Keller and D. S. Cohen, Some positone problems suggested by nonlinear heat generation, J. Math. Mech. 16 (1967), 1361-1376. Zbl0152.10401
  15. [15] P. H. Rabinowitz, Multiple critical points of perturbed symmetric functionals, Trans. Amer. Math.Soc. 272 (1982), 753-769. Zbl0589.35004

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