Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/395
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Article Citation - WoS: 2Citation - Scopus: 7Triple Positive Solutions for M-Point Boundary-Value Problems of Dynamic Equations on Time Scales With P-Laplacian(Texas State Univ, 2015) Dogan, AbdulkadirIn this article we study the existence of positive solutions for m-point dynamic equation on time scales with p-Laplacian. We prove that the boundary-value problem has at least three positive solutions by applying the five functionals fixed-point theorem. An example demonstrates the main results.Article Citation - WoS: 10Citation - Scopus: 12Positive Solutions of the P-Laplacian Dynamic Equations on Time Scales With Sign Changing Nonlinearity(Texas State Univ, 2018) Dogan, AbdulkadirThis article concerns the existence of positive solutions for p-Laplacian boundary value problem on time scales. By applying fixed point index we obtain the existence of solutions. Emphasis is put on the fact that the nonlinear term is allowed to change sign. An example illustrates our results.Article Citation - WoS: 7Citation - Scopus: 9On the Existence of Positive Solutions of the P-Laplacian Dynamic Equations on Time Scales(Wiley, 2017-01-26) Dogan, AbdulkadirIn this paper, we investigate the existence of positive solutions for a nonlinear m-point boundary value problem for the p-Laplacian dynamic equations on time scales, by applying a Krasnosel'skii's fixed point theorem. As an application, an example is included to demonstrate themain results. Copyright (C) 2017 John Wiley & Sons, Ltd.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 Citation - Scopus: 3Existence of Positive Solutions for P-Laplacian an M-Point Boundary Value Problem Involving the Derivative on Time Scales(Texas State Univ, 2014) Dogan, AbdulkadirWe are interested in the existence of positive solutions for the p-Laplacian dynamic equation on time scales (phi(P)(u(Delta)(t)))(V) a(t)f (t, u Delta(t), (t)) = 0, t is an element of (0,T)(T), subject to the multipoint boundary condition, u(0) = Sigma(m-2)(i=1) alpha iu, (xi(i)) = u Delta(T) = 0, where phi(p)(S) = vertical bar s vertical bar p(-2) s, p > 1, xi i is an element of [0, T](T,) 0 < xi 1 < xi 2 < . . . < xi m-2 < p(T). 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.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.Article Citation - WoS: 17Citation - Scopus: 13Existence of Multiple Positive Solutions for P-Laplacian Multipoint Boundary Value Problems on Time Scales(Springeropen, 2013-08-07) Dogan, AbdulkadirIn this paper, we consider p-Laplacian multipoint boundary value problems on time scales. By using a generalization of the Leggett-Williams fixed point theorem due to Bai and Ge, we prove that a boundary value problem has at least three positive solutions. Moreover, we study existence of positive solutions of a multipoint boundary value problem for an increasing homeomorphism and homomorphism on time scales. By using fixed point index theory, sufficient conditions for the existence of at least two positive solutions are provided. Examples are given to illustrate the results. MSC: 34B15, 34B16, 34B18, 39A10.Article Citation - WoS: 4Citation - Scopus: 4Eigenvalue Problems for Nonlinear Third-Order M-Point P-Laplacian Dynamic Equations on Time Scales(Wiley, 2014-08-18) Dogan, AbdulkadirThis work deals with the existence and uniqueness of a nontrivial solution for the third-order p-Laplacian m-point eigenvalue problems on time scales. We find several sufficient conditions of the existence and uniqueness of nontrivial solution of eigenvalue problems when lambda is in some interval. The proofs are based on the nonlinear alternative of Leray-Schauder. To illustrate the results, some examples are included. Copyright (C) 2014 John Wiley & Sons, Ltd.