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Book Review
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Book Information
Author(s):
C. V. Pao
Title:
Nonlinear parabolic and elliptic equations
Additional book information:
Plenum Press, New York and London, 1992, xv+777 pp., US$125.00. ISBN 0-306-44343-0
References:
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- O. Perron, Ein Neuer Existenzbeweis fur sie Integrale der Differentialgleichung
, Math. Ann. 76 (1915), 471-484. MR 1511836 - [2]
- M. Nagumo, On principally linear elliptic differential equations of second order, Osaka. J. Math. 6 (1954), 207-229. MR 0070014 (16:1116a)
- [3]
- K. Ako, On the Dirichlet problem of quasi-linear elliptic differential equations of second order, J. Math. Soc. Japan 13 (1961), 45-62. MR 0147758 (26:5272)
- [4]
- H. B. Keller, Elliptic boundary value problems suggested by nonlinear diffusion processes, Arch. Rational Mech. Anal. 5 (1969), 363-381. MR 0255979 (41:639)
- [5]
- H. Amann, On the existence of positive solutions of nonlinear elliptic boundary value problems, Indiana Univ. Math. J. 21 (1971), 125-146. MR 0296498 (45:5558)
- [6]
- K. Schmitt, Boundary value problems for quasilinear second order elliptic equations, Nonlinear Anal. 2 (1978), 263-309. MR 512661 (80b:35064)
- [7]
- D. Sattinger, Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Math. J. 21 (1972), 979-1000. MR 0299921 (45:8969)
- [8]
- C. V. Pao, Successive approximations of some nonlinear initial-boundary value problems, SIAM J. Math. Anal. 5 (1974), 91-102. MR 0339507 (49:4265)
- [9]
- -, Positive solutions of a nonlinear boundary value problem of parabolic type, J. Differential Equations 22 (1976), 145-163. MR 0422876 (54:10862)
- [10]
- J. P. Puel, Existence, comportement à l'infini et stabilité dans certaines problèmes quasilinéaires elliptiques et paraboliques d'ordre 2, Ann. Scuola Norm. Sup. Pisa Cl. Sci (4) 3 (1976), 89-119. MR 0399654 (53:3497)
- [11]
- H. A. Levine and L. E. Payne, Nonexistence theorem for the heat equation with nonlinear boundary conditions and for porous medium equation backward in time, J. Differential Integral Equations 16 (1974), 319-334. MR 0470481 (57:10235)
- [12]
- A. Friedman and B. McLeod, Blowup of positive solutions of semilinear heat equations, Indiana Univ. Math. J. 34 (1985), 425-447. MR 783924 (86j:35089)
- [13]
- S. Carl, On existence of extremal weak solutions for a class of quasilinear parabolic problems, Differential Integral Equations 6 (1993), 1493-1505. MR 1235207 (94h:35124)
- [14]
- H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev. 18 (1976), 620-709. MR 0415432 (54:3519)
Additional Information:
Reviewer(s):
Jerrold
Bebernes
Review Information:
Journal:
Bull. Amer. Math. Soc.
32
(1995),
166-169.
DOI:
10.1090/S0273-0979-1995-00568-9
PII:
S 0273-0979(1995)00568-9
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