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Classification of solutions of some nonlinear elliptic equations. (English) Zbl 0768.35025
The paper concerns the equations \(\Delta u+u^ p=0\), \(x\in\mathbb{R}^ n\), \(n\geq 3\), and \(\Delta u+\exp u=0\), \(x\in\mathbb{R}^ 2\), \(\int_{\mathbb{R}^ 2} \exp u(x)dx<\infty\).

MSC:
35J60 Nonlinear elliptic equations
35C05 Solutions to PDEs in closed form
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[1] C. Li, Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on unbounded domain , to appear in Comm. Partial Differential Equations. · Zbl 0741.35014 · doi:10.1080/03605309108820770
[2] B. Gidas, W. M. Ni, and L. Nirenberg, Symmetry of positive solutions of nonlinear elliptic equations in \(\mathbf R\spn\) , Mathematical analysis and applications, Part A ed. L. Nachbin, Adv. in Math. Suppl. Stud., vol. 7, Academic Press, New York, 1981, pp. 369-402. · Zbl 0469.35052
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