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Öğe Existence and comparison results for first order periodic implicit difference equations with maxima(Taylor & Francis Ltd, 2002) Atici, FM; Cabada, A; Ferreiro, JBIn this paper, we establish comparison results (maximum principles) which allow us to use the monotone method and the method of upper and lower solutions in order to build convergent sequences to the solutions of difference equations of the type Deltau(k) = f(k,u(k+1), max(lepsilon(kh+1,....,k+1)) u(l)), k epsilon I, u(0) = u(T), with -u(k), I = {0,1,...,T-1} and f epsilon l(I x R x R,R).Öğe Existence of positive solutions of nonlinear discrete Sturm-Liouville problems(Pergamon-Elsevier Science Ltd, 2000) Atici, FMWe are concerned with proving the existence of positive solutions of two-point boundary value problems for the nonlinear discrete Sturm-Liouville equation Ly(t) := -Delta[p(t - 1)Delta y(t - 1)] + q(t)y(t) = f(t,y(t)). We will use some results for differentiable operators along a certain cone in a Banach space. Useful results concerning Green's functions for general two-point boundary value problems for Ly(t) := -Delta[p(t - 1)Delta y(t - 1)] + q(t)y(t) = 0 will also be given. (C) 2000 Elsevier Science Ltd. All rights reserved.Öğe The generalized quasilinearization method and three point boundary value problems on time scales(Pergamon-Elsevier Science Ltd, 2005) Atici, FM; Topal, SGIn this paper, we study the convergence of monotone sequences of iterates for nonlinear second order dynamic equations with three point boundary conditions on time scales. We prove that it is possible to construct two sequences converging to the unique solution of the three point boundary value problem from above and below with high rate of convergence. (c) 2004 Elsevier Ltd. All rights reserved.Öğe On Green's functions and positive solutions for boundary value problems on time scales(Elsevier Science Bv, 2002) Atici, FM; Guseinov, GSIn this paper we offer a form of self-adjoint differential equations on time scales so that the associated Green's function is found symmetric in the usual sense. For this purpose together with the delta derivative we employ the nabla derivative as well, We introduce the concepts of Lebesgue delta and nabla integrals on time scales. Next, sign properties of the Green's function are investigated and existence results for positive solutions of nonlinear boundary value problems are established. Upper and lower bounds for these positive solutions also are given, (C) 2002 Elsevier Science B.V. All rights reserved.Öğe On Lyapunov inequality in stability theory for Hill's equation on time scales(Gordon Breach Sci Publ Ltd, 2000) Atici, FM; Guseinov, GS; Kaymakcalan, BIn this paper we obtain sufficient conditions for instability and stability to hold for second order linear Delta -differential equations on time scales with periodic coefficients.Öğe On the existence of positive solutions for nonlinear differential equations with periodic boundary conditions(Elsevier Science Bv, 2001) Atici, FM; Guseinov, GSWe prove the existence of positive solutions of second-order nonlinear differential equations on a finite interval with periodic boundary conditions and give upper and lower bounds for these positive solutions. Obtained results yield positive periodic solutions of the equation on the whole real axis, provided that the coefficients are periodic. (C) 2001 Elsevier Science B.V. All rights reserved.Öğe Positive periodic solutions for nonlinear difference equations with periodic coefficients(Academic Press Inc, 1999) Atici, FM; Guseinov, GSWe prove the existence of positive solutions of second-order nonlinear difference equations on a finite discrete segment with periodic boundary conditions. Obtained results yield positive periodic solutions of the equation on the whole discrete axis, provided that the coefficients are periodic. (C) 1999 Academic Press.
