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Eigenvalues for iterative systems of nonlinear m-point boundary value problems on time scales

Ilkay Y Karaca1* and Fatma Tokmak12

Author Affiliations

1 Department of Mathematics, Ege University, Bornova, Izmir, 35100, Turkey

2 Department of Mathematics, Gazi University, Teknikokullar, Ankara, 06500, Turkey

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Boundary Value Problems 2014, 2014:63  doi:10.1186/1687-2770-2014-63

Published: 21 March 2014


In this paper, we determine the eigenvalue intervals of the parameters <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/63/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/63/mathml/M1">View MathML</a> for which there exist positive solutions of the iterative systems of m-point boundary value problems on time scales. The method involves an application of Guo-Krasnosel’skii fixed point theorem. We give an example to demonstrate our main results.

MSC: 34B18, 34N05.

Green’s function; iterative system; eigenvalue interval; time scales; boundary value problem; fixed point theorem; m-point; positive solution