Über gewöhnliche Differentialungleichungen zweiter Ordnung
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- by Roland Lemmert PDF
- Proc. Amer. Math. Soc. 83 (1981), 720-724 Request permission
Abstract:
A theorem about the separation of sub- and superfunctions $\upsilon$ and $w$ by solutions of an ordinary differential equation of second order is proved, where $\upsilon \geqslant w$ throughout the given interval. Examples show that the condition imposed on the right side $f$ of the equation is sharp, and that an analogous theorem is not true for Laplace’s equation, even in the case $f \equiv 0,\upsilon$ sub- and $w$ superharmonic.References
- E. F. Beckenbach, Generalized convex functions, Bull. Amer. Math. Soc. 43 (1937), no. 6, 363–371. MR 1563543, DOI 10.1090/S0002-9904-1937-06549-9 M. Nagumo, Über die Differentialgleichung $y'' = f(x,y,y’)$, Proc. Phys. Math. Soc. Japan 19 (1937), 861-866.
- Keith W. Schrader, Differential inequalities for second- and third-order equations, J. Differential Equations 25 (1977), no. 2, 203–215. MR 457828, DOI 10.1016/0022-0396(77)90200-5
- A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 720-724
- MSC: Primary 34A30
- DOI: https://doi.org/10.1090/S0002-9939-1981-0630027-4
- MathSciNet review: 630027