Imed Bachar, Habib Maagli
We prove the existence and uniqueness, and study the global behavior of a positive continuous solution to the superlinear second-order differential equation
where a,b are nonnegative constants such that a+b>0, A is a continuous function on , positive and continuously differentiable on such that 1/A is integrable on [0,1] and . Here , for and g(t,s) is a nonnegative continuous function satisfying suitable integrability condition. Our Approach is based on estimates of the Green's function and a perturbation argument. Finally two illustrative examples are given.
Submitted October 11, 2014. Published January 5, 2015.
Math Subject Classifications: 34B15, 34B18, 34B27.
Key Words: Second order differential equation; boundary value problem; half-line; Green's function; positive solution.
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| Imed Bachar |
King Saud University, College of Science
Mathematics Department, P.O. Box 2455
Riyadh 11451, Saudi Arabia
| Habib Mâagli |
King Abdulaziz University, College of Sciences and Arts
Rabigh Campus, Department of Mathematics P.O. Box 344
Rabigh 21911, Saudi Arabia
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