Doğan, Abdülkadir

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Job Title:Prof. Dr.
Email Address:abdulkadir.dogan@agu.edu.tr
Main Affiliation:02.01. Mühendislik Bilimleri
Status: Current Staff
ORCID:ORCID Profile0000-0002-3195-4718
Scopus ID:Scopus Profile7101805539
YÖK Akademik: 5D7811E6EB327925
Google Scholar:Google Scholar ProfilevfRBaoMAAAAJ
Web of Science ID:Web of Science ProfileA-9812-2013
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Abdulkadir DOĞAN Dogan, A.
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Now showing 1 - 10 of 21
  • Article
    Citation - WoS: 7
    Citation - Scopus: 9
    On the Existence of Positive Solutions of the P-Laplacian Dynamic Equations on Time Scales
    (Wiley, 2017-01-26) Dogan, Abdulkadir
    In 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: 1
    Citation - Scopus: 10
    Existence of Three Positive Solutions for an M-Point Boundary-Value Problem on Time Scales
    (Texas State Univ, 2013) Dogan, Abdulkadir
    We 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.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Triple 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
    Citation - WoS: 10
    Citation - Scopus: 12
    Positive Solutions of the P-Laplacian Dynamic Equations on Time Scales With Sign Changing Nonlinearity
    (Texas State Univ, 2018) Dogan, Abdulkadir
    This 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: 17
    Citation - Scopus: 13
    Existence of Multiple Positive Solutions for P-Laplacian Multipoint Boundary Value Problems on Time Scales
    (Springeropen, 2013-08-07) Dogan, Abdulkadir
    In 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: 7
    Citation - Scopus: 7
    Positive Solutions of Nonlinear Multi-Point Boundary Value Problems
    (Springer, 2018-05-17) Dogan, Abdulkadir
    This 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
    Positive Solutions of Multipoint Φ-Laplacian BVPS With First-Order Derivative Dependence
    (World Scientific, 2023) Bachouche, Kamal; Tair, Hocine; Doǧan, Abdülkadir Muhittin
    This paper concerns existence of positive solutions for a second-order boundary value problem of Sturm-Liouville type associated with a φ-Laplacian operator and posed on a bounded interval. Existence results are obtained by an adapted version of the Krasnosel'skii's fixed point theorem of cone expansion and compression. Some examples illustrate our results. © 2023 Elsevier B.V., All rights reserved.
  • 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, Abdulkadir
    In 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 - Scopus: 3
    Existence of Positive Solutions for P-Laplacian an M-Point Boundary Value Problem Involving the Derivative on Time Scales
    (Texas State Univ, 2014) Dogan, Abdulkadir
    We 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
    Citation - WoS: 1
    Existence of Countably Many Positive Solutions for Nonlinear Boundary Value Problems on Time Scales
    (Natural Sciences Publishing Corp-nsp, 2014-09-01) Dogan, Abdulkadir
    In this paper, we consider the existence of countably many positive solutions for nonlinear singular boundary value problem on time scales. By using the fixed-point index theory and a new fixed-point theorem in cones, the sufficient conditions for the existence of countably many positive solutions are established.

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