## Duke Mathematical Journal

### Solutions of superlinear elliptic equations and their Morse indices, I

#### 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

#### 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

#### 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.