Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 235, pp. 112.
Combined effects in nonlinear singular secondorder differential
equations on the halfline
Imed Bachar
Abstract:
We consider the existence, uniqueness and the asymptotic behavior
of positive continuous solutions to the secondorder boundaryvalue 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
email: abachar@ksu.edu.sa

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