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Öğe Existence of multiple positive solutions for the system of higher order boundary value problems on time scales(Pergamon-Elsevier Science Ltd, 2010) Cetin, Erbil; Topal, S. GulsanIn this paper, by applying fixed point theorems in cones and under suitable conditions, we present the existence of single and multiple solutions for system of higher order boundary value problems on time scales. (C) 2009 Elsevier Ltd. All rights reserved.Öğe Existence of Positive Periodic Solutions in Shifts delta(+/-) for a Nonlinear First Order Functional Dynamic Equation on Time Scales(Univ Nis, Fac Sci Math, 2016) Cetin, Erbil; Topal, F. SerapLet T subset of R be a periodic time scale in shifts delta(+/-) with period P is an element of [t(0),infinity)(T). In this paper we consider the nonlinear functional dynamic equation of the form x(del)(t) = a(t)x(t) - lambda b(t)f(x(h(t))), t is an element of T. By using the Krasnoselskii, Avery-Henderson and Leggett-Williams fixed point theorems, we present different sufficient conditions for the nonexistence and existence of at least one, two or three positive periodic solutions in shifts delta(+/-) of the above problem on time scales. We extend and unify periodic differential, difference, h-difference and q-difference equations and more by a new periodicity concept on time scales.Öğe Existence of positive solutions for Lidstone boundary value problems on time scales(Springer, 2023) Cetin, Erbil; Topal, Fatma Serap; Agarwal, Ravi P.Let T subset of R be a time scale. The purpose of this paper is to present sufficient conditions for the existence of multiple positive solutions of the following Lidstone boundary value problem on time scales: (-1)(n)y(Delta(2n)) (t) = f (t, y(t)), t is an element of [a, b]T, y(Delta(2i)) (alpha) = y(Delta(2i)) (sigma(2n-2i)(b)) i = 0, i = 0,1,..., n - 1. Existence of multiple positive solutions is established using fixed point methods. At the end some examples are also given to illustrate our results.Öğe Existence of positive solutions of a Sturm-Liouville BVP on an unbounded time scale(Taylor & Francis Ltd, 2008) Topal, S. Gulsan; Yantir, Ahmet; Cetin, ErbilA fixed point theorem of Guo-Krasnoselskii type is used to establish existence results for the nonlinear Sturm-Liouville dynamic equation (p(t)x(Delta))(del) + lambda phi(t)f(t,x(t)) = 0 with the boundary conditions on an unbounded time scale. Later on the positivity and the boundedness of the solutions are obtained by imposing some conditions on f.Öğe Existence of solutions for a delay singular high order fractional boundary value problem with sign-changing nonlinearity(Univ Nis, Fac Sci Math, 2023) Cetin, Erbil; Topal, Fatma SerapThis paper consider the existence of at least one positive solution of a Riemann-Liouville fractional delay singular boundary value problem with sign-changing nonlinerty. To establish sufficient conditions we use the Guo-Krasnosel'skii fixed point theorem.Öğe Existence of solutions for a first-order nonlocal boundary value problem with changing-sign nonlinearity(Scientific Technical Research Council Turkey-Tubitak, 2015) Cetin, Erbil; Topal, Fatma SerapThis work is concerned with the existence of positive solutions to a nonlinear nonlocal first-order multipoint problem. Here the nonlinearity is allowed to take on negative values, not only positive values.Öğe Existence of solutions for fourth order three-point boundary value problems on a half-line(Univ Szeged, Bolyai Institute, 2015) Cetin, Erbil; Agarwal, Ravi P.In this paper, we apply Schauder's fixed point theorem, the upper and lower solution method, and topological degree theory to establish the existence of unbounded solutions for the following fourth order three-point boundary value problem on a half-line x''''(t) + q(t) f(t, x(t), x'(t), x ''(t), x'''(t)) = 0, t is an element of (0, +infinity), x ''(0) = A, x(eta) = B-1, x'(eta) = B-2, x'''(+infinity) = C, where eta is an element of (0, +infinity), but fixed, and f : [0, +infinity) x R-4 -> R satisfies Nagumo's condition. We present easily verifiable sufficient conditions for the existence of at least one solution, and at least three solutions of this problem. We also give two examples to illustrate the importance of our results.Öğe Existence of Solutions for Nonlinear Four-Point p-Laplacian Boundary Value Problems on Time Scales(Hindawi Publishing Corporation, 2009) Topal, S. Gulsan; Ozen, O. Batit; Cetin, ErbilWe are concerned with proving the existence of positive solutions of a nonlinear second-order four-point boundary value problem with a p-Laplacian operator on time scales. The proofs are based on the fixed point theorems concerning cones in a Banach space. Existence result for p-Laplacian boundary value problem is also given by the monotone method. Copyright (C) 2009 S. Gulsan Topal et al.Öğe Existence of solutions to fourth-order differential equations with deviating arguments(Springeropen, 2015) Naceri, Mostepha; Agarwal, Ravi P.; Cetin, Erbil; Amir, El HaffafIn this paper, we consider fourth-order differential equations on a half-line with deviating arguments of the form u((4))(t) + q(t) f (t, [u(t)], [u'(t)], [u ''(t)], u'''(t)) = 0, 0 < t < + infinity, with the boundary conditions u(0) = A, u' (0) = B, u '' (t) -au'''(t) = theta(t), -tau <= t <= 0; u'''(+infinity) = C. We present sufficient conditions for the existence of a solution between a pair of lower and upper solutions by using Schauder's fixed point theorem. Also, we establish the existence of three solutions between two pairs of lower and upper solutions by using topological degree theory. An important feature of our existence criteria is that the obtained solutions may be unbounded. We illustrate the importance of our results through two simple examples.Öğe Existence of solutions to fourth-order differential equations with deviating arguments(Springeropen, 2015) Naceri, Mostepha; Agarwal, Ravi P.; Cetin, Erbil; Amir, El HaffafIn this paper, we consider fourth-order differential equations on a half-line with deviating arguments of the form u((4))(t) + q(t) f (t, [u(t)], [u'(t)], [u ''(t)], u'''(t)) = 0, 0 < t < + infinity, with the boundary conditions u(0) = A, u' (0) = B, u '' (t) -au'''(t) = theta(t), -tau <= t <= 0; u'''(+infinity) = C. We present sufficient conditions for the existence of a solution between a pair of lower and upper solutions by using Schauder's fixed point theorem. Also, we establish the existence of three solutions between two pairs of lower and upper solutions by using topological degree theory. An important feature of our existence criteria is that the obtained solutions may be unbounded. We illustrate the importance of our results through two simple examples.Öğe Existence of solutions to fourth-order differential equations with deviating arguments(Springeropen, 2015) Naceri, Mostepha; Agarwal, Ravi P.; Cetin, Erbil; Amir, El HaffafIn this paper, we consider fourth-order differential equations on a half-line with deviating arguments of the form u((4))(t) + q(t) f (t, [u(t)], [u'(t)], [u ''(t)], u'''(t)) = 0, 0 < t < + infinity, with the boundary conditions u(0) = A, u' (0) = B, u '' (t) -au'''(t) = theta(t), -tau <= t <= 0; u'''(+infinity) = C. We present sufficient conditions for the existence of a solution between a pair of lower and upper solutions by using Schauder's fixed point theorem. Also, we establish the existence of three solutions between two pairs of lower and upper solutions by using topological degree theory. An important feature of our existence criteria is that the obtained solutions may be unbounded. We illustrate the importance of our results through two simple examples.Öğe Existence Results for Solutions of Integral Boundary Value Problems on Time Scales(Hindawi Publishing Corporation, 2013) Cetin, Erbil; Topal, F. SerapThis paper deals with the existence of solutions for integral boundary value problems (IBVPs) on time scales. We provide sufficient conditions for the existence of solutions by using Schauder fixed point theorem in a cone. Existence result for this problem is also given by the method of upper and lower solutions.Öğe Existence Results for Solutions of Integral Boundary Value Problems on Time Scales(Hindawi Publishing Corporation, 2013) Cetin, Erbil; Topal, F. SerapThis paper deals with the existence of solutions for integral boundary value problems (IBVPs) on time scales. We provide sufficient conditions for the existence of solutions by using Schauder fixed point theorem in a cone. Existence result for this problem is also given by the method of upper and lower solutions.Öğe Higher order boundary value problems on time scales(Academic Press Inc Elsevier Science, 2007) Cetin, Erbil; Topal, S. GulsanIn this paper we study the existence of solutions for Lidstone boundary value problems on time scale. Firstly, by using Schauder fixed point theorem in a cone, we obtain the existence of solutions to a Lidstone boundary value problem (LBVP). Secondly, existence result for this problem is also given by the monotone method. Finally, by using Krasnosel'skii fixed point theorem, it is proved that the LBVP has a positive solution. (c) 2006 Elsevier Inc. All rights reserved.Öğe The Lower and Upper Solution Method for Three-Point Boundary Value Problems with Integral Boundary Conditions on a Half-Line(Univ Nis, Fac Sci Math, 2018) Akcan, Ummahan; Cetin, ErbilThis paper deal with the following second-order three-point boundary value problem with integral boundary condition on a half-line u ''(x) + q(x) f(x, u(x), u' (x)) = 0, x is an element of(0, +infinity), u(0) = lambda integral(eta)(0) u(s)ds, u'(+infinity) = C, where lambda > 0, 0 < lambda(eta) < 1 and f : [0; +infinity) X R-2 -> R satisfies a Nagumo's condition which plays an important role in the nonlinear term depend on the first-order derivative explicitly. By using Schauder's fixed point theorem, the upper and lower solution method and topological degree theory, first we give sufficient conditions for the existence of at least one solution and next at least three solutions of the above problem. Moreover, an example is included to demonstrate the efficiency of the main results.Öğe Lyapunov type inequalities for second-order forced dynamic equations with mixed nonlinearities on time scales(Springer-Verlag Italia Srl, 2017) Agarwal, Ravi P.; Cetin, Erbil; Ozbekler, AbdullahIn this paper, we present some newHartman and Lyapunov inequalities for second-order forced dynamic equations on time scales T with mixed nonlinearities: x(Delta Delta)(t) + Sigma(n)(k=1) qk (t)vertical bar x(sigma) (t)vertical bar (alpha k-1) x(sigma) (t) = f (t); t is an element of [t(0), infinity)(T), where the nonlinearities satisfy 0 < alpha(1) < ... < alpha(m) < 1 < alpha(m+1) < ... < alpha(n) < 2. No sign restrictions are imposed on the potentials qk, k = 1, 2, ... , n, and the forcing term f. The inequalities obtained generalize and compliment the existing results for the special cases of this equation in the literature.Öğe Periodic Solutions in Shifts delta(+/-) for a Nonlinear Dynamic Equation on Time Scales(Hindawi Publishing Corporation, 2012) Cetin, Erbil; Topal, F. SerapLet T subset of R be a periodic time scale in shifts delta(+/-). We use a fixed point theorem due to Krasnosel'ski(sic) to show that nonlinear delay in dynamic equations of the form x(Delta)(t) = -a(t)x(sigma)(t) + b(t)x(Delta)(delta(-)(k, t))delta(Delta)(-)(k, t) + q(t, x(t), x(delta_(k, t)), t is an element of T, has a periodic solution in shifts delta(+/-). We extend and unify periodic differential, difference, h-difference, and q-difference equations and more by a new periodicity concept on time scales.Öğe Positive periodic solutions in shifts for a nonlinear first-order functional dynamic equation on time scales(Springer International Publishing Ag, 2014) Cetin, ErbilLet be a periodic time scale in shifts with period . We consider the existence of positive periodic solutions in shifts for the nonlinear functional dynamic equation of the form x (t) = - a(t) xs (t) +.b(t) f (t, x(h(t))), t. T using the cone theory techniques. We extend and unify periodic differential, difference, h-difference and q-difference equations and more by a new periodicity concept on time scales.Öğe Solutions for 2n(th) order lidstone BVP on time scales(Scientific Technical Research Council Turkey-Tubitak, 2009) Cetin, Erbil; Topal, S. GuelsanIn this paper, we prove the existence of solutions for nonlinear Lidstone boundary value problems by using the monotone method on time scales and also we show the existence of at least one positive solution if f is either superlinear of sublinear by the fixed point theorem in a Banach space.Öğe Symmetric positive solutions of fourth order boundary value problems for an increasing homeomorphism and homomorphism on time-scales(Pergamon-Elsevier Science Ltd, 2012) Cetin, Erbil; Topal, F. SerapLet T subset of R be a symmetric bounded time-scale, with a = min T, b = max T. We consider the following fourth order boundary value problem phi(-px(Delta del))(Delta del) (t) + f(t, x(t)) = 0, t is an element of T-kappa 2(kappa 2), x(a) = x(b) = 0, x(Delta del) (sigma(a)) = x(Delta del) (rho(b)) = 0 for a suitable function p and an increasing homeomorphism and homomorphism phi. By using the Krasnosel'skii fixed point theorem, we present sufficient conditions for the existence of at least one or two symmetric positive solutions of the above problem on time-scales. As applications, two examples are given to illustrate the main results. (C) 2011 Elsevier Ltd. All rights reserved.
