Exact asymptotic behavior of the positive solutions for some singular Dirichlet problems on the half line

Date

2016-02-17

Authors

Maagli, Habib
Alsaedi, Ramzi
Zeddini, Noureddine

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Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

In this article, we give an exact behavior at infinity of the unique solution to the following singular boundary value problem -1/A (Au′)′ = q(t)g(u), t ∈ (0, ∞), u > 0, lim t→0 A(t)u′(t) = 0, lim t→0 u(t) = 0. Here A is a nonnegative continuous function on [0, ∞), positive and differentiable on (0, ∞) with lim t→0 g′ (t) ∫t0 ds/g(s) = -Cg ≤ 0 and the function q is a nonnegative continuous, satisfying 0 < α1 = lim t→∞ inf q(t)/h(t) ≤ lim t→∞ sup q(t)/h(t) = α2 < ∞, where h(t) = ct-λ exp(∫t1 y(s)/s ds), λ ≥ 2, c > 0 and y is continuous on [1, ∞) such that lim t→∞ y(t) = 0.

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Keywords

Singular nonlinear boundary value problems, Positive solution, Exact asymptotic behavior, Karamata regular variation theory

Citation

Mâagli, H., Alsaedi, R., & Zeddini, N. (2016). Exact asymptotic behavior of the positive solutions for some singular Dirichlet problems on the half line. <i>Electronic Journal of Differential Equations, 2016</i>(49), pp. 1-14.

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Attribution 4.0 International

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