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Nonlinear partial differential inequalities. (English) Zbl 0201.13703

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[1] Akô, K., & T. Kusano, On bounded solutions of second order elliptic differential equations. Journal Fac. Sci. Univ. of Tokyo, Sec. I, 11, 1, 29–37 (1964). · Zbl 0143.14005
[2] Atkinson, F. V., On a theorem of K. Yôsida. Proc. Japan Academy 28, 327–329 (1952). · Zbl 0047.34401 · doi:10.3792/pja/1195570894
[3] Bohn, S. Elwood, & Lloyd K. Jackson, The Liouville theorem for a quasi-linear elliptic partial differential equation. Trans. Amer. Math. Soc. 104, 392–397 (1962). · Zbl 0119.30704 · doi:10.1090/S0002-9947-1962-0139840-6
[4] Collatz, L., Aufgaben monotoner Art. Arch. Math. 3, 366–376 (1952). · Zbl 0048.09802 · doi:10.1007/BF01899376
[5] Collatz, L., Funktionalanalysis und numerische Mathematik. Berlin-Göttingen-Heidelberg: Springer 1964.
[6] Friedman, A., Partial Differential Equations of Parabolic Type. Prentice-Hall 1964. · Zbl 0144.34903
[7] Habetha, K., Über das Maximumprinzip und verwandte Fragen bei Lösungen elliptischparabolischer Differentialgleichungen 2. Ordnung. Math. Zeit. 81, 308–325 (1963). · Zbl 0192.19802 · doi:10.1007/BF01111578
[8] Haviland, E. K., A note on unrestricted solutions of the differential equation \(\Delta\)u=f(u). J. London Math. Soc. 26, 210–214 (1951). · Zbl 0043.10203 · doi:10.1112/jlms/s1-26.3.210
[9] Hopf, E., Elementare Bemerkungen über die Lösung partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus. Sitzber. Akad. der Wiss., Berlin, 1927, 56–75. · JFM 53.0454.02
[10] Keller, J. B., On solutions of \(\Delta\)u=f(u). Comm. Pure Appl. Math. 10, 503–510 (1957). · Zbl 0090.31801 · doi:10.1002/cpa.3160100402
[11] Meyers, Norman, & James Serrin, The exterior Dirichlet problem for second order elliptic partial differential equations. J. Math. Mech. 9, 513–538 (1960). · Zbl 0094.29701
[12] Nehari, Zeev, A differential inequality. J. d’Anal. Math. 14, 297–302 (1965). · Zbl 0139.05701 · doi:10.1007/BF02806396
[13] Nirenberg, L., A strong maximum principle for parabolic equations. Comm. Pure and Appl. Math. 6, 167–177 (1953). · Zbl 0050.09601 · doi:10.1002/cpa.3160060202
[14] Osserman, R., On the inequality \(\Delta\)u(u). Pacific J. Math. 7, 1641–1647 (1957). · Zbl 0083.09402 · doi:10.2140/pjm.1957.7.1641
[15] Piepenbrink, J., Differential inequalities in unbounded regions. Dissertation, University of California, Los Angeles, 1969.
[16] Redheffer, Raymond, Elementary remarks on problems of mixed type. J. Math. Phys. 53, 1–14 (1964). · Zbl 0152.10803 · doi:10.1002/sapm19644311
[17] Serrin, J., On the Harnack inequality for linear elliptic equations. Journal d’Anal. Math. 1956, 292–308. · Zbl 0070.32302
[18] Serrin, J., Notes on boundary layer theory. University of Minnesota (excerpt made available to us at U.C.L.A.).
[19] Serrin, J., The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables. Phil. Trans. Roy. Soc. London 264, 413–496 (1969). · Zbl 0181.38003 · doi:10.1098/rsta.1969.0033
[20] Velte, W., Eine Anwendung des Nirenbergschen Maximumprinzips für parabolische Differentialgleichungen in der Grenzschichttheorie. Arch. Rational Mech. Anal. 5, 420–431 (1960). · Zbl 0098.40204 · doi:10.1007/BF00252919
[21] Výborný, R., Über das erweiterte Maximumprinzip. Czechoslovak J. Math. 14 (89), 116–121 (1964). · Zbl 0145.36801 · doi:10.1007/BF01688665
[22] Walter, W., Über ganze Lösungen der Differentialgleichung \(\Delta\)u=f(u), Jahresber. Deutsch. Math. Verein 57, 94–102 (1955). · Zbl 0066.34402
[23] Walter, W., Differential- und Integralgleichungen. Springer Tracts in Nat. Phil. 2. BerlinGöttingen-Heidelberg: Springer 1964.
[24] Wittich, H., Ganze Lösungen der Differentialgleichung \(\Delta\)u=f(u). Jahresber. Deutsch. Math. Verein 57, 94–102 (1955).
[25] Yôsida, K., A theorem of Liouville’s type for meson equation. Proc. Japan Academy 27, 334–339 (1951). · Zbl 0043.09701 · doi:10.3792/pja/1195571352
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