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- W1488821607 abstract "It is well-known that good bounds for solutions of nonlinear differential equations are difficult to obtain. In this paper, we establish a theorem comparing non-negative solutions (having identical initial values) of the equations u″(t)+q(t)u p (t)+r(t)u(t) = 0 and v″(t)+k(t)q(t)v p (t)+r(t)u(t) = 0, respectively. If q(t),r(t) ≥ 0, k(t) ≥ 1, k(t) is non-decreasing, and the first equation satisfies a certain uniqueness criterion, our result asserts that u(t) ≥ v(t). Both the uniqueness assumption on the equation and the monotonicity requirement on k(t) are necessary. A particular case of this theorem plays a central role in a recent paper of Atkinson and Peletier in the study of asymptotic behavior of nonlinear elliptic equations involving a critical exponent. A simple corollary of our result provides information on the same type of equations with subcritical exponents." @default.
- W1488821607 created "2016-06-24" @default.
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- W1488821607 date "1992-01-01" @default.
- W1488821607 modified "2023-09-23" @default.
- W1488821607 title "A Comparison Result and Elliptic Equations Involving Subcritical Exponents" @default.
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- W1488821607 doi "https://doi.org/10.1007/978-1-4612-0393-3_22" @default.
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