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Transactions of the American Mathematical Society

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Existence and nonoscillation theorems for an Emden-Fowler equation with deviating argument


Author: William F. Trench
Journal: Trans. Amer. Math. Soc. 294 (1986), 217-231
MSC: Primary 34K15; Secondary 34C15
DOI: https://doi.org/10.1090/S0002-9947-1986-0819944-9
MathSciNet review: 819944
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Abstract: Sufficient conditions are given for a generalized Emden-Fowler equation with deviating argument to have nonoscillatory solutions with prescribed asymptotic behavior as $ t \to \infty $. The integrability condition on the nonlinear term requires only conditional convergence, supplemented by a condition on the order of convergence, which is automatically satisfied in some important special cases. The exponent in the nonlinear term may be any real number. The deviating argument is not assumed to be purely advanced or retarded, and, in some cases, need not tend to infinity. Some of the results are global, in that the desired solution is shown to exist on a given interval, rather than only for sufficiently large $ t$.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0819944-9
Keywords: Emden-Fowler nonoscillatory equation, asymptotic, global existence, local existence
Article copyright: © Copyright 1986 American Mathematical Society

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