Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Comparison theorems for second-order nonlinear differential equations


Author: Stanley B. Eliason
Journal: Quart. Appl. Math. 29 (1971), 391-402
MSC: Primary 34C10; Secondary 34B15
DOI: https://doi.org/10.1090/qam/402177
MathSciNet review: 402177
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Abstract: Comparison theorems for a nonlinear eigenvalue problem as well as a Lyapunov type of inequality are derived. They are used to establish upper and lower bounds for various integral functionals associated with real solutions of the nonlinear boundary value problem $ y'' + p\left( x \right){y^{2n + 1}} = 0, y\left( a \right) = y'\left( b \right) = 0$, where $ a < b$ are real, $ n$ is a positive integer and $ p$ is positive and continuous on $ \left[ {a,b} \right]$. Some of the results are analogues of a distance between zeros problem for the linear case of $ n = 0$.


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DOI: https://doi.org/10.1090/qam/402177
Article copyright: © Copyright 1971 American Mathematical Society


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