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On the asymptotic behavior of solutions ofu″ − (1 +f(t))u=0

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Summary

The asymptotic behavior of the solutions ofu″ − (1 + f(t))u=0 is treated under the assumptions thatf(t)0 as t → ∞ and that\(\mathop \smallint \limits^\infty \left| {f(t)} \right|^n< \infty \) for somen>0. The method used consists of converting the above equation into a non-linear equation of first order via the substitutionv=u′/u, and applying standard techniques of non-linear differential equation theory.

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Pervenuta in redazione il 15 maggio 1950.

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Bellman, R. On the asymptotic behavior of solutions ofu″ − (1 +f(t))u=0. Annali di Matematica 31, 83–91 (1950). https://doi.org/10.1007/BF02428257

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Keywords

  • Differential Equation
  • Asymptotic Behavior
  • Standard Technique
  • Equation Theory
  • Differential Equation Theory