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Lyapunov functions and autonomous differential equations in a Banach space

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References

  1. S. K. Aalto, An iterative procedure for solving nonlinear equations in a Banach space,J. Math. Anal. Appl. 24 (1968), 689–691.

    Google Scholar 

  2. L. P. Belluce andW. A. Kirk, Nonexpansive mappings and fixed-points in Banach spaces,Illinois J. Math. 11 (1967), 474–479.

    Google Scholar 

  3. D. W. Boyd andJ. S. W. Wong, On nonlinear contractions,Proc. Amer. Math. Soc. 20 (1969), 458–464.

    Google Scholar 

  4. F. E. Browder, Nonexpansive nonlinear operators in a Banach space,Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1041–1044.

    Google Scholar 

  5. F. E. Browder, Nonlinear equations of evolution and nonlinear accretive operators in Banach spaces,Bull. Amer. Math. Soc. 73 (1967), 867–874.

    Google Scholar 

  6. W. A. Coppel,Stability and Asymptotic Behavior of Differential Equations, D. C. Heath and Co., Boston, 1965.

    Google Scholar 

  7. R. DeMarr, Common fixed-points for commuting contraction mappings,Pacific J. Math. 13 (1963), 1139–1141.

    Google Scholar 

  8. P. Hartman, Generalized Lyapunov functions and functional equations,Ann. Math. Pura Appl. 69 (1965). 305–320.

    Google Scholar 

  9. V. Lakshmikanthan andS. Leela,Differential and Integral Inequalities I, Academic Press, New York, 1969.

    Google Scholar 

  10. R. H. Martin, Jr., A Global existence theorem for autonomous differential equations in a Banach space,Proc. Amer. Math. Soc. 26 (1970), 307–314.

    Google Scholar 

  11. R. H. Martin, Jr., A theorem on critical points and global asymptotic stability,J. Math. Anal. Appl. 32 (1970), in press.

  12. H. Murakami, On nonlinear ordinary and evolution equations,Funkcial. Ekvac. 9 (1966), 151–162.

    Google Scholar 

  13. M. Z. Nashed, A decomposition relative to convex sets,Proc. Amer. Math. Soc. 19 (1968), 782–786.

    Google Scholar 

  14. Chi-Lin Yen, Sufficient conditions for the existence of a rest point for a nonlinear semigroup of contractions,Notices Amer. Math. Soc. 17 (1970), 1031.

    Google Scholar 

  15. E. Zarantonello, The closure of the numerical range contains the spectrum,Pacific J. Math. 22 (1967), 575–595.

    Google Scholar 

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  1. Department of Mathematics, North Carolina State University, 27607, Raleigh, North Carolina, USA

    R. H. Martin Jr.

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  1. R. H. Martin Jr.
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Martin, R.H. Lyapunov functions and autonomous differential equations in a Banach space. Math. Systems Theory 7, 66–72 (1973). https://doi.org/10.1007/BF01824808

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