In this paper we establish the existence of single and multiple solutions to the semiposi-tone discrete Dirichlet boundary value problem ∆ 2 y(i − 1) + µf (i, y(i)) = 0, i ∈ {1, 2, ..., T } y(0) = y(T + 1) = 0, where µ > 0 is a constant and our nonlinear term f (i, u) may be singular at u = 0. .

This paper investigates the solvability of discrete Dirichlet boundary value problems by the lower and upper solution method. Here, the second order difference equation with a nonlinear right hand side f is studied and f(t, u, v) can have a superlinear growth both in u and in v. Moreover, the growth conditions on f are one-sided. We compute a priori bounds on solutions to the discrete problem a...

The linear spectral problem associated with the inverse solution of a nite discrete nonlinear Schrr odinger chain is studied in the semiclassical limit. The discrete spectral problem is a recursion relation for a vector quantity, with boundary conditions, depending on initial data and a spectral parameter. WKB analysis is performed and then interpreted for the case that the quantities in the ch...

We present an existence theorem for nonlinear ordinary differential equations of first order with nonlinear boundary conditions. The result includes, for instance, the initial value problem, the final value problem, and the antiperiodic boundary value problem. The main novelty of the method lies in that it unifies different techniques for initial or boundary conditions.

Most real world engineering design problems, such as cross-country water mains, include combinations of continuous, discrete, and binary value decision variables. Very often, the binary decision variables associate with the presence and/or absence of some nominated alternatives or project’s components. This study extends an existing continuous Ant Colony Optimization (ACO) algorithm to simultan...

Chaotic dynamics has been hailed as the third great scientific revolution of the 20th century, along with relativity and quantum mechanics [1]. In this paper, we consider the one-dimensional wave equation with the initial-boundary value problem on the unit interval. The boundary condition at the left endpoint is linear homogeneous, injecting energy into the system, while the boundary condition ...

in this paper, a numerical method is developed for solving a linear sixth order boundaryvalue problem (6vbp ) by using the hyperbolic uniform spline of order 3 (lower order). thereis proved to be first-order convergent. numerical results confirm the order of convergencepredicted by the analysis.

this article is devoted to the study of existence and multiplicity of positive solutions to aclass of nonlinear fractional order multi-point boundary value problems of the type−dq0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,u(0) = 0, u(1) =m−2∑ i=1δiu(ηi),where dq0+ represents standard riemann-liouville fractional derivative, δi, ηi ∈ (0, 1) withm−2∑i=1δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ∞...