We consider the existence, uniqueness and the asymptotic behavior of positive continuous solutions to the second-order boundary-value problem
where , A is a continuous function on , positive and differentiable on such that and . Here and for , is a nonnegative continuous function in such that there exists c%>0 satisfying for t>0,
where and , , , and is continuous on for some such that . The comparable asymptotic rate of determines the asymptotic behavior of the solution.
Submitted May 3, 2015. Published September 11, 2015.
Math Subject Classifications: 34B15, 34B18, 34B27.
Key Words: Green's function; Karamata regular variation theory; positive solution; Schauder fixed point theorem.
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| Imed Bachar |
King Saud University College of Science
Mathematics Department, P.O. Box 2455
Riyadh 11451, Saudi Arabia
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