## Duke Mathematical Journal

### Classification of solutions of some nonlinear elliptic equations

#### Article information

Source
Duke Math. J., Volume 63, Number 3 (1991), 615-622.

Dates
First available in Project Euclid: 20 February 2004

https://projecteuclid.org/euclid.dmj/1077296071

Digital Object Identifier
doi:10.1215/S0012-7094-91-06325-8

Mathematical Reviews number (MathSciNet)
MR1121147

Zentralblatt MATH identifier
0768.35025

Subjects
Primary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc.
Secondary: 35J60: Nonlinear elliptic equations

#### Citation

Chen, Wenxiong; Li, Congming. Classification of solutions of some nonlinear elliptic equations. Duke Math. J. 63 (1991), no. 3, 615--622. doi:10.1215/S0012-7094-91-06325-8. https://projecteuclid.org/euclid.dmj/1077296071

#### References

• [1] C. Li, Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on unbounded domain, to appear in Comm. Partial Differential Equations.
• [2] B. Gidas, W. M. Ni, and L. Nirenberg, Symmetry of positive solutions of nonlinear elliptic equations in $\bf R\spn$, Mathematical analysis and applications, Part A ed. L. Nachbin, Adv. in Math. Suppl. Stud., vol. 7, Academic Press, New York, 1981, pp. 369–402.
• [3] H. Berestycki and L. Nirenberg, Some qualitative properties of solutions of semilinear elliptic equations in cylindrical domains, to appear.
• [4] M. Obata, The conjectures on conformal transformations of Riemannian manifolds, J. Differential Geometry 6 (1971/72), 247–258.
• [5] L. Caffarelli, B. Gidas, and J. Spruck, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, preprint.
• [6] B. Gidas and J. Spruck, Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math. 34 (1981), no. 4, 525–598.
• [7] W. Ding, personal communication.
• [8] H. Brezis and F. Merle, Estimates on the solutions of $\Delta u=v(x) \exp u(x)$ on $R^2$, preprint.