WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/394
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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: 4Citation - Scopus: 5The Existence of Positive Solutions for a Semipositone Second-Order M-Point Boundary Value Problem(Dynamic Publishers, inc, 2015) Dogan, AbdulkadirIn this paper, we study the existence of positive solutions to boundary value problem {u '' + lambda f(t,u)=0, t is an element of(0,1); u(0)=Sigma(m-2)(i-1) alpha (i)u(xi(i)), u'(1) = Sigma (m-2)(i=1) beta(i) u'(xi(i)), where xi(i) is an element of(0, 1), 0 < xi(1) < xi(2) < ... < xi(m-2) < 1, alpha(i), beta(i) is an element of[0,infinity), lambda is positive parameter. By using Krasnoserskii's fixed point theorem, we provide sufficient conditions for the existence of at least one positive solution to the above boundary value problem.Article Solutions to Nonlinear Second-Order Three-Point Boundary Value Problems of Dynamic Equations on Time Scales(Tubitak Scientific & Technological Research Council Turkey, 2019-05-29) Dogan, AbdulkadirIn this paper, we consider existence criteria of three positive solutions of three-point boundary value problems for p-Laplacian dynamic equations on time scales. To show our main results, we apply the well-known Leggett-Williams fixed point theorem. Moreover, we present some results for the existence of single and multiple positive solutions for boundary value problems on time scales, by applying fixed point theorems in cones. The conditions we used in the paper are different from those in [Dogan A. On the existence of positive solutions for the one-dimensional p-Laplacian boundary value problems on time scales. Dynam Syst Appl 2015; 24: 295-304].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: 7Positive Solutions of Nonlinear Multi-Point Boundary Value Problems(Springer, 2018-05-17) Dogan, AbdulkadirThis paper deals with the existence of positive solutions of nonlinear differential equation subject to the boundary conditions By using Schauder's fixed point theorem, we show that it has at least one positive solution if f is nonnegative and continuous. Positive solutions of the above boundary value problem satisfy theHarnack inequality inf(0 <= t <= 1) u(t) >= gamma parallel to u parallel to(infinity.)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 Citation - WoS: 4Citation - Scopus: 5On the Existence of Positive Solutions for the Second-Order Boundary Value Problem(Pergamon-Elsevier Science Ltd, 2015-11) Dogan, AbdulkadirThis paper is concerned with the existence of positive solutions to a second order boundary value problem. By imposing growth conditions on f and using a generalization of the Leggett-Williams fixed point theorem, we prove the existence of at least three symmetric positive solutions. (C) 2015 Elsevier Ltd. All rights reserved.Article Citation - WoS: 2Citation - Scopus: 3On the Existence of Positive Solutions for the One-Dimensional P-Laplacian Boundary Value Problems on Time Scales(Dynamic Publishers, inc, 2015) Dogan, AbdulkadirIn this paper, we study the following p-Laplacian boundary value problems on time scales {(phi(p)(u(Delta)(t)))(del) + a(t)f(t, u(t), u(Delta)(t)) = 0, t is an element of [0,T](T), u(0) - B-0(u(Delta)(0)) = 0, u(Delta)(T) = 0, where phi(p)(u) = vertical bar u vertical bar(p-2)u, for p > 1. We prove the existence of triple positive solutions for the one-dimensional p-Laplacian boundary value problem by using the Leggett-Williams fixed point theorem. The interesting point in this paper is that the non-linear term f is involved with first-order derivative explicitly. An example is also given to illustrate the main result.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 - WoS: 1Citation - Scopus: 10Existence of Three Positive Solutions for an M-Point Boundary-Value Problem on Time Scales(Texas State Univ, 2013) Dogan, AbdulkadirWe study an m-point boundary-value problem on times scales. By using a fixed point theorem, we prove the existence of at least three positive solutions, under suitable growth conditions imposed on the nonlinear term. An example is given to illustrate our results.