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

Trench, William F.

doi:10.1090/S0002-9947-1986-0819944-9

Existence and nonoscillation theorems for an Emden-Fowler equation with deviating argument
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by William F. Trench

Trans. Amer. Math. Soc. 294 (1986), 217-231

DOI: https://doi.org/10.1090/S0002-9947-1986-0819944-9

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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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