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Lyapunov methods and equations of parabolic type

Part of the Lecture Notes in Mathematics book series (LNM,volume 322)

Keywords

  • Lyapunov Function
  • Equilibrium Solution
  • Nonlinear Partial Differential Equation
  • Functional Versus
  • Solution Curve

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References

  1. Amann, H., On the existence of positive solutions of nonlinear elliptic boundary value problems, Indiana Univ. Math. J. 21, 125–146 (1971).

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  2. Aris, R., On stability criteria of chemical reactor engineering, Chem. Eng. Sci. 24, 149–169 (1969).

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  3. Chafee, N. and Infante, E.F., A bifurcation problem for a nonlinear partial differential equation of parabolic type, to appear.

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  4. Hempel, J. A., Multiple solutions for a class of nonlinear boundary value value problems, Indiana Univ. Math. J. 20, 983–996 (1971).

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  5. Keller, H. B. and Cohen, D.S., Some positone problems suggested by nonlinear heat generation, Jour. Math. Mech. 16, 1361–1376 (1967).

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  6. Stattinger, D. H., Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Math. J. 21, 979–1000 (1972).

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  7. Simpson, R. B. and Cohen, D. S., Positive solutions of nonlinear elliptic eigenvalue problems, J. Math. Mech. 19, 895–910 (1970).

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  8. Vainberg, M. M., Variational methods for the study of nonlinear operators, Holden-Day, San Francisco 1964.

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  9. Zubov, V., Methods of A. M. Lyapunov and their application, Noordhoff, 1964.

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© 1973 Springer Verlag

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Auchmuty, J.F.G. (1973). Lyapunov methods and equations of parabolic type. In: Stakgold, I., Joseph, D.D., Sattinger, D.H. (eds) Nonlinear Problems in the Physical Sciences and Biology. Lecture Notes in Mathematics, vol 322. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060559

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  • DOI: https://doi.org/10.1007/BFb0060559

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06251-6

  • Online ISBN: 978-3-540-38558-5

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