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References
Browder, F. E.: The solvability of non-linear functional equations. Duke math. J.30, 557–566 (1963)
Carasso, A.: Finite-difference methods and the eigenvalue problem for nonselfadjoint Sturm-Liouville operators. Math. Comput.23, 717–729 (1969)
Carasso, A.: A posteriori bounds in the numerical solution of midly nonlinear parabolic equations. Math. Comput.24, 785–792 (1970)
Carasso, A., Parter, S. V.: An analysis of “boundary-value techniques” for parabolic problems. Math. Comput.24, 315–340 (1970)
Carasso, A.: Long-range numerical solution of midly non-linear parabolic equations. Numerische Math.16, 304–321 (1971)
Ceremnyh, Ju. N.: Estimate of a solution of the first boundary problem for parabolic equations of second order. Soviet Math., Doklady9, 551–555 (1968)
Courant, R., Hilbert, D.: Methoden der Mathematischen Physik, Vol. 1 New York: Interscience 1953
Friedman, A.: Convergence of solutions of parabolic equations to a steady state. J. Math. Mech.8, 57–76 (1959)
Friedman, A.: Asymptotic behaviour of solutions of parabolic equations. J. Math. Mech.8, 387–392 (1959)
Friedman, A.: Asymptotic behavior of solutions of parabolic equations of any order. Acta math.106, 1–43 (1961)
Friedman, A.: Partial Differential Equations of Parabolic Type. Englewood Cliffs: Prentice-Hall 1964
Friedman, A.: Remarks on nonlinear parabolic equations. In: Proceedings of Symposia in Applied Mathematics (New York 1964) Vol. XVII, pp. 3–23. Providence: American Mathematical Society 1965
Fujita, H.: On the nonlinear equations Δu+e u=0 and ∂v/∂t=Δv+e v. Bull. Amer. Math. Soc.75, 132–135 (1969)
Gekeler, E.: Zur Berechnung periodischer Lösungen bei parabolischen Randwert-problemen. In: Numerische, insbesondere approximationstheoretische Behandlung von Funktionalgleichungen, Lecture Notes in Math. Berlin-Heidelberg-New York: Springer (to appear)
Greenspan, D.: Lectures on the Numerical Solution of Linear, Singular, and Nonlinear Differential Equations. Englewood Cliffs: Prentice-Hall 1968
Isaacson, E., Keller, H. B.: Analysis of Numerical Methods. New York: John Wiley 1966
Kolesov, Ju. S.: Periodic solutions of quasilinear parabolic equations of second order. Trans. Moscow math. Soc.21, 114–146 (1970)
Kolodner, I. I., Pederson, R. N.: Pointwise bounds for solutions of semilinear parabolic equations. J. diff. Equations2, 353–364 (1966)
Kružkov, S. N.: Periodic solutions of nonlinear second order parabolic equations (Russian). Differencial'nye Uravnenija6, 731–740 (1970)
Lees, M.: Approximate solution of parabolic equations. J. Soc. industr. appl. Math.7, 167–183 (1959)
Mikhailov, V. P.: The Dirichlet problem and the first mixed problem for a parabolic equation. Soviet Math. Doklady2, 1204–1207 (1961)
Minty, G. J.: Monotone (nonlinear) operators in Hilbert space. Duke math. J.29, 341–346 (1962)
Minty, G. J.: On a “monotonicity” method for the solution of nonlinear equations in Banach spaces. Proc. nat. Acad. Sci. USA50, 1038–1041 (1963)
Oddson, J. K.: On the rate of decay of solutions of parabolic differential equations. Numerische Math.7, 155–158 (1965)
Osborne, M. R.: A note on the numerical solution of a periodic parabolic problem. Numerische Math.7, 155–158 (1965)
Šmulev, I. I.: Periodic solutions of the first boundary problem for parabolic equations. Amer. math. Soc., Translat., II Ser.79, 215–229 (1969)
Tee, G. J.: An application ofp-cyclic matrices. Numerische Math.6, 143–158 (1964)
Ton, B. A.: Mixed initial boundary-value problems for semi-linear parabolic equations. Duke math. J.34, 481–491 (1967)
Varga, R. S.: Matrix Iterative Analysis. Englewood Cliffs: Prentice-Hall 1962
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Gekeler, E. Long-range and periodic solutions of parabolic problems. Math Z 134, 53–66 (1973). https://doi.org/10.1007/BF01219091
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DOI: https://doi.org/10.1007/BF01219091