Duke Mathematical Journal

Solutions of superlinear elliptic equations and their Morse indices, I

A. Harrabi, S. Rebhi, and A. Selmi

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Article information

Source
Duke Math. J. Volume 94, Number 1 (1998), 141-157.

Dates
First available in Project Euclid: 19 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077230080

Digital Object Identifier
doi:10.1215/S0012-7094-98-09407-8

Mathematical Reviews number (MathSciNet)
MR1635912

Zentralblatt MATH identifier
0952.35042

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

Citation

Harrabi, A.; Rebhi, S.; Selmi, A. Solutions of superlinear elliptic equations and their Morse indices, I. Duke Math. J. 94 (1998), no. 1, 141--157. doi:10.1215/S0012-7094-98-09407-8. https://projecteuclid.org/euclid.dmj/1077230080


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References

  • [1] A. Bahri and P. L. Lions, Solutions of superlinear elliptic equations and their Morse indices, Comm. Pure Appl. Math. 45 (1992), no. 9, 1205–1215.
  • [2] B. Gidas, W.-M. Ni, and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), no. 3, 209–243.
  • [3] B. Gidas and J. Spruck, A priori bounds for positive solutions of nonlinear elliptic equations, Comm. Partial Differential Equations 6 (1981), no. 8, 883–901.
  • [4] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Grundlehren Math. Wiss., vol. 224, Springer-Verlag, New York, 1977.
  • [5] S. I. Pohožaev, Eigenfunctions of $\Delta u+\lambda f(u)=0$, Soviet Math. Dokl. 6 (1965), 1408–1411.

See also

  • See also: Salem Rebhi. Errata to “Solutions of super-linear elliptic equations and their Morse indices, I,” Duke Math. J. 94 (1998), 141–157. Duke Math. J. Vol. 162, No. 1 (2013), pp. 199–200.
  • See also: A. Harrabi, S. Rebhi, A. Selmi. Solutions of superlinear elliptic equations and their Morse indices, II. Duke Math. J. Vol. 94, No. 1 (1998), pp. 159–179.