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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:
- [1]
- O. Perron, Ein Neuer Existenzbeweis fur sie Integrale der Differentialgleichung $y'=f(x,y)$, Math. Ann. \textbf{76} (1915), 471--484.
- [2]
- M. Nagumo, On principally linear elliptic differential equations of second order, Osaka. J. Math. \textbf{6} (1954), 207--229.
- [3]
- K. Ako, On the Dirichlet problem of quasi-linear elliptic differential equations of second order, J. Math. Soc. Japan \textbf{13} (1961), 45--62.
- [4]
- H. B. Keller, Elliptic boundary value problems suggested by nonlinear diffusion processes, Arch. Rational Mech. Anal. \textbf{5} (1969), 363--381.
- [5]
- H. Amann, On the existence of positive solutions of nonlinear elliptic boundary value problems, Indiana Univ. Math. J. \textbf{21} (1971), 125--146.
- [6]
- K. Schmitt, Boundary value problems for quasilinear second order elliptic equations, Nonlinear Anal. \textbf{2} (1978), 263--309.
- [7]
- D. Sattinger, Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Math. J. \textbf{21} (1972), 979--1000.
- [8]
- C. V. Pao, Successive approximations of some nonlinear initial-boundary value problems, SIAM J. Math. Anal. \textbf{5} (1974), 91--102.
- [9]
- C. V. Pao, Positive solutions of a nonlinear boundary value problem of parabolic type, J. Differential Equations \textbf{22} (1976), 145--163.
- [10]
- J. P. Puel, Existence, comportement \`a l'infini et stabilit\'e dans certaines probl\`emes quasilin\'eaires elliptiques et paraboliques d'ordre \RM 2, Ann. Scuola Norm. Sup. Pisa Cl. Sci (4) \textbf{3} (1976), 89--119.
- [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 \textbf{16} (1974), 319--334.
- [12]
- A. Friedman and B. McLeod, Blowup of positive solutions of semilinear heat equations, Indiana Univ. Math. J. \textbf{34} (1985), 425--447.
- [13]
- S. Carl, On existence of extremal weak solutions for a class of quasilinear parabolic problems, Differential Integral Equations \textbf{6} (1993), 1493--1505.
- [14]
- H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev. \textbf{18} (1976), 620--709.
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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