In this paper, by using four functionals fixed point theorem and five functionals fixed point theorem, we study the existence of at least one positive solution and three positive solutions respectively of a fourth-order four-point boundary value problem with alternating coefficient on a time scale. Examples are also included to illustrate our results.

}, keywords = {34B15}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/24/25-DSA-313-326.pdf}, author = {ILKAY YASLAN KARACA} } @article {57, title = {EXISTENCE OF THREE POSITIVE SOLUTIONS FOR M-POINT TIME SCALE BOUNDARY VALUE PROBLEMS ON INFINITE INTERVALS}, journal = {Dynamic Systems and Applications}, volume = {20}, year = {2011}, month = {2011}, pages = {13}, chapter = {355}, abstract = {In this paper, by using the Leggett-Williams fixed point theorem and Five Functionals fixed point theorem, we establish the existence of three positive solutions for m-point time scale boundary value problems on infinite intervals. As an application, we also give some examples to demonstrate our results.

}, keywords = {34B10, 39A10}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/20/24-DSA-778.pdf}, author = {ILKAY YASLAN KARACA and FATMA TOKMAK} } @article {133, title = {FOURTH-ORDER M-POINT BOUNDARY VALUE PROBLEMS ON TIME SCALES}, journal = {Dynamic Systems and Applications}, volume = {19}, year = {2010}, month = {2010}, pages = {21}, chapter = {249}, abstract = {Let T be a time scale with [a, b] ⊂ T. We establish criteria for existence of one or more than one positive solutions of the non-eigenvalue problem (0.1) y △4 (t) - q(t)y ∆2 (σ(t)) = f(t, y(t)), t ∈ [a, b] ⊂ T, y(a) = Pm-2 i=1 aiy(ξi), y(σ 2 (b)) = Pm-2 i=1 biy(ξi), y ∆2 (a) = Pm-2 i=1 aiy ∆2 (ξi), y∆2 (σ 2 (b)) = Pm-2 i=1 biy ∆2 (ξi), where ξi ∈ (a, b), ai , bi ∈ [0, $\infty$) (for i ∈ {1, 2, . . . , m-2}) are given constants. Later, we consider the existence and multiplicity of positive solutions for the eigenvalue problem y △4 (t) - q(t)y ∆2 (σ(t)) = λf(t, y(t)) with the same boundary conditions. We shall also obtain criteria which lead to nonexistence of positive solutions. In both problems, we will use Krasnoselskii fixed point theorem.

}, keywords = {34B10, 39A10}, issn = {1056-2176}, url = {https://acadsol.eu/dsa/articles/19/19-DSA-257.pdf}, author = {ILKAY YASLAN KARACA and OZLEM YILMAZ} }