Electron. J. Diff. Equ.,
Vol. 2014 (2014), No. 37, pp. 110.
Existence of positive solutions for pLaplacian an
mpoint boundary value problem involving the derivative on time scales
Abdulkadir Dogan
Abstract:
We are interested in the existence of positive solutions for the Laplacian
dynamic equation on time scales,
subject to the multipoint boundary condition,
where
,
,
,
.
By using fixed point theorems, we prove the existence of at least three
nonnegatvie solutions, two of them positive, to the above boundary value
problem. The interesting point is the nonlinear term f is involved with
the first order derivative explicitly.
An example is given to illustrate the main result.
Submitted December 3, 2013. Published January 30, 2014.
Math Subject Classifications: 34B15, 34B16, 34B18, 39A10.
Key Words: Time scales; boundary value problem; pLaplacian;
positive solution; fixed point theorem.
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Abdulkadir Dogan
Department of Applied Mathematics
Faculty of Computer Sciences
Abdullah Gul University, Kayseri, 38039 Turkey
Tel: +90 352 224 88 00 Fax: +90 352 338 88 28
email: abdulkadir.dogan@agu.edu.tr

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