WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/394
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Article Citation - WoS: 1Citation - Scopus: 1Triple Positive Solutions of M-Point Boundary Value Problem on Time Scales With P-Laplacian(Iranian Mathematical Soc, 2017) Dogan, A.In this paper, we consider the multipoint boundary value problem for one-dimensional p-Laplacian dynamic equation on time scales. We prove the existence at least three positive solutions of the boundary value problem by using the Avery and Peterson fixed point theorem. The interesting point is that the non-linear term f involves a first-order derivative explicitly. Our results are new for the special cases of difference equations and differential equations as well as in the general time scale setting.Article Multiple Positive Solutions of Nonlinear M-Point Dynamic Equations for P-Laplacian on Time Scales(Tubitak Scientific & Technological Research Council Turkey, 2016) Dogan, AbdulkadirIn this paper, we study the existence of positive solutions of a nonlinear m-point p-Laplacian dynamic equation (phi(p) (x(Delta)(t)))(del) w(t)f (t,x(t), x(Delta)(t)) = 0, t(1) < m-1 X(ti) - B-0 (Sigma m-1 i=2 a(i)x(Delta)(t(i))) = 0, x(Delta) (tm) = 0, or x(Delta)(t(1)) - 0, x(t(m)) + B-1(Sigma m-1 i=2 b(i)s(Delta)(t(i))) -0, where phi(p)(s) =vertical bar s vertical bar(P-2) s, p > 1. Sufficient conditions for the existence of at least three positive solutions of the problem are obtained by using a fixed point theorem. The interesting point is the nonlinear term f is involved with the first order derivative explicitly. As an application, an example is given to illustrate the result.Article Existence of Positive Solutions for Nonlinear Multipoint P-Laplacian Dynamic Equations on Time Scales(Tubitak Scientific & Technological Research Council Turkey, 2020-05-08) Dogan, AbdulkadirIn this paper, we investigate the existence of positive solutions for nonlinear multipoint boundary value problems for p-Laplacian dynamic equations on time scales with the delta derivative of the nonlinear term. Sufficient assumptions are obtained for existence of at least twin or arbitrary even positive solutions to some boundary value problems. Our results are achieved by appealing to the fixed point theorems of Avery-Henderson. As an application, an example to demonstrate our results is given.