Monotone positive solutions for a class of second-order nonlinear differential equations

Ertem, T.
Zafer, Ağacık
It is shown that the second-order nonlinear differential equation


Asymptotic behavior of solutions of differential equations with piecewise constant arguments
Akhmet, Marat (Elsevier BV, 2008-09-01)
The main goal of the work is to obtain sufficient conditions for the asymptotic equivalence of a linear system of ordinary differential equations and a quasilinear system of differential equations with piecewise constant argument.
Dynamic programming for a Markov-switching jump-diffusion
Azevedo, N.; Pinheiro, D.; Weber, Gerhard Wilhelm (Elsevier BV, 2014-09-01)
We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump-diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman's optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton-Jacobi-Belman equation, which turns out to be a partial in...
Hyperbolic conservation laws on manifolds. An error estimate for finite volume schemes
Lefloch, Philippe G.; Okutmuştur, Baver; Neves, Wladimir (Springer Science and Business Media LLC, 2009-07-01)
Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L (1)-error estimate for a class of finite volume schemes allowing for the approximation of entropy solutions to the initial value problem. The error in the L (1) norm is of order h (1/4) at most, where h represents the maximal diameter of elements in the family of geodesic triangulations. The proof relies on a suitable generalization of Cockburn, Coquel, and LeFloch's theo...
Perron's theorem for linear impulsive differential equations with distributed delay
Akhmet, Marat; Zafer, A. (Elsevier BV, 2006-08-15)
In this paper it is shown that under a Perron condition trivial solution of linear impulsive differential equation with distributed delay is uniformly asymptotically stable.
Accurate numerical bounds for the spectral points of singular Sturm-Liouville problems over 0 < x < infinity
Taşeli, Hasan (Elsevier BV, 2004-03-01)
The eigenvalues of singular Sturm-Liouville problems defined over the semi-infinite positive real axis are examined on a truncated interval 0<x<l as functions of the boundary point l. As a basic theoretical result, it is shown that the eigenvalues of the truncated interval problems satisfying Dirichlet and Neumann boundary conditions provide, respectively, upper and lower bounds to the eigenvalues of the original problem. Moreover, the unperturbed system in a perturbation problem, where l remains sufficient...
Citation Formats
T. Ertem and A. Zafer, “Monotone positive solutions for a class of second-order nonlinear differential equations,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, pp. 672–681, 2014, Accessed: 00, 2020. [Online]. Available: