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Petry, Walter

Iterative Lösung gewisser nichtlinearer Operatorgleichungen mit Anwendung auf quasilineare Differentialgleichungen. (German) Zbl 0248.35104

Aequationes Math. 8, 113-135 (1972).
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Cited in 2 Documents

MSC:

35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
35A35 Theoretical approximation in context of PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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Full Text: DOI EuDML

References:

[1] Browder, F. E.,Nonlinear Elliptic Boundary Value Problems, Bull. Amer. Math. Soc.69, 862–874 (1963). · Zbl 0127.31901 · doi:10.1090/S0002-9904-1963-11068-X
[2] Browder, F. E. andPetryshyn, W. V.,The Topological Degree and Galerkin Approximations for Noncompact Operators in Banach Spaces, Bull. Amer. Math. Soc.74, 641–646 (1968). · Zbl 0164.17003 · doi:10.1090/S0002-9904-1968-11973-1
[3] Košelev, A. I.,Convergence of the Method of Successive Approximations for Quasilinear Elliptic Equations, Soviet Math. Dokl.3, 219–222 (1962).
[4] Kratochvil, A.,Les methodes approximatives de la Solution des Equations Elliptiques Non Lineaires, Comment. Math. Univ. Carolinae9 (3), 455–510 (1968). · Zbl 0169.20005
[5] Petry, W.,Ein iteratives Verfahren zur Bestimmung einer Lösung gewisser nichtlinearer Operatorgleichungen im Hilbertraum mit Anwendung auf Hammersteinsche Integralgleichungssysteme, Math. Ann.187, 127–149 (1970). · doi:10.1007/BF01350178
[6] Petry, W.,Ein globales Iterationsverfahren, ZAMM51, T68-T70 (1971). · Zbl 0221.65089
[7] Petry, W.,Die Linienmethode zum Nachweis von Existenz und Eindeutigkeit einer Lösung der nichtlinearen Evolutionsgleichung mit nichtlinearer Nebenbedingung, Habilitationsschrift TH Aachen SS 1970 (Kernforschungsanlag Jülich, Jül-716–MA, Dezember 1970).
[8] Petry, W.,Eine Variante des Newtonschen Iterationsverfahrens, ZAMM50, T74-T75 (1970).
[9] Petry, W.,Eine Verallgemeinerung des Newtonschen Iterationsverfahrens, Computing7, 25–45 (1971). · Zbl 0221.65090 · doi:10.1007/BF02279939
[10] Petry, W.,Ein Iterationsverfahren zum Lösen von Randwertproblemen nichtlinearer Differentialgleichungen, Computing5, 27–44 (1970). · Zbl 0187.11102 · doi:10.1007/BF02234248
[11] Petry, W.,Verallgemeinerte Hammersteinsche Gleichung und quasilineare Randwertprobleme, Math. Nachr. · Zbl 0203.46101
[12] Petryshyn, W. V.,On the Approximation-Solvability of Nonlinear Equations, Math. Ann.177, 156–164 (1968). · Zbl 0162.20301 · doi:10.1007/BF01350791
[13] Petryshyn, W. V.,On a Fixed Point Theorem for Nonlinear P-compact Operators in Banach Spaces, Bull. Amer. Math. Soc.72, 329–334 (1966). · Zbl 0142.11201 · doi:10.1090/S0002-9904-1966-11519-7
[14] Petryshyn, W. V.,On Nonlinear P-compact Operators in Banach Spaces with Applications to Constructive Fixed-point Theorems, J. Math. Anal. Appl.15, 228–242 (1966). · Zbl 0149.10602 · doi:10.1016/0022-247X(66)90114-4
[15] Petryshyn, W. V.,Further Remarks on Nonlinear P-compact Operators in Banach Spaces, J. Math. Anal. Appl.16, 243–254 (1966). · Zbl 0149.10603 · doi:10.1016/0022-247X(66)90169-7
[16] Petryshyn, W. V. andTucker, T. S.,On the Functional Equations Involving Nonlinear Generalized P-compact Operators, Trans. Amer. Math. Soc.135, 343–373 (1969) (MR40, # 804). · Zbl 0174.19501
[17] Ortega, J. M. andRheinboldt, W. C.,Iterative Solution of Nonlinear Equations in Several Variables (Academic Press, New York–London 1970).
[18] Petryshyn, W. V.,Construction of Fixed Points of Demicompact Mappings in Hilbert Spaces, J. Math. Anal. Appl.14, 276–284 (1966). · Zbl 0138.39802 · doi:10.1016/0022-247X(66)90027-8
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