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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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[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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