Comparison theorems for nonselfadjoint differential equations based on integral inequalities
HTML articles powered by AMS MathViewer
- by Kurt Kreith PDF
- Proc. Amer. Math. Soc. 34 (1972), 105-109 Request permission
Abstract:
In a variant of the classical Sturmian comparison theorem for selfadjoint Sturm-Liouville equations, A. Ju. Levin has replaced the pointwise conditions on the coefficients by an integral inequality. This theorem is generalized to apply to nonselfadjoint differential equations of the form \[ u'' + b(x)u’ + c(x)u = 0.\]References
- A. Ju. Levin, A comparison principle for second-order differential equations, Soviet Math. Dokl. 1 (1960), 1313–1316. MR 0124563
- E. Kamke, A new proof of Sturm’s comparison theorems, Amer. Math. Monthly 46 (1939), 417–421. MR 326, DOI 10.2307/2303035
- C. A. Swanson, A comparison theorem for elliptic differential equations, Proc. Amer. Math. Soc. 17 (1966), 611–616. MR 201781, DOI 10.1090/S0002-9939-1966-0201781-2
- Kurt Kreith, A comparison theorem for general elliptic equations with mixed boundary conditions, J. Differential Equations 8 (1970), 537–541. MR 265737, DOI 10.1016/0022-0396(70)90026-4
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 34 (1972), 105-109
- MSC: Primary 34C10
- DOI: https://doi.org/10.1090/S0002-9939-1972-0304770-5
- MathSciNet review: 0304770