## On the nonlinear equations $$\Delta u + e^ u = 0$$ and $$\partial v/\partial t = \Delta v + e^ v$$.(English)Zbl 0216.12101

### MSC:

 35J65 Nonlinear boundary value problems for linear elliptic equations
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### References:

 [1] R. Courant and D. Hilbert, Methods of mathematical physics. Vol. 2, Interscience, New York, 1962. · Zbl 0099.29504 [2] I. M. Gel$$^{\prime}$$fand, Some problems in the theory of quasi-linear equations, Uspehi Mat. Nauk 14 (1959), no. 2 (86), 87 – 158 (Russian). [3] Eberhard Hopf, A remark on linear elliptic differential equations of second order, Proc. Amer. Math. Soc. 3 (1952), 791 – 793. · Zbl 0048.07802 [4] Tosio Kato, On the upper and lower bounds of eigenvalues, J. Phys. Soc. Japan 4 (1949), 334 – 339.
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