Initial-boundary value problems for 1-dimensional ‘completely integrable’ equations can be solved via an extension of the inverse scattering method, which is due to Fokas and his collaborators. A crucial feature of this method is that it requires the values of more boundary data than given for a well-posed problem. In the case of cubic NLS, knowledge of the Dirichet data suffices to make the pr...

In this article we gain solvability to a nonlinear, second-order difference equation with discrete Neumann boundary conditions. Our methods involve new inequalities on the right-hand side of the difference equation and Schaefer’s Theorem in the finite-dimensional space setting. © 2006 Elsevier Inc. All rights reserved.

We describe an approach to the numerical solution of the integral equations of scattering theory on planar curves with corners. It is rather comprehensive in that it applies to a wide variety of boundary value problems; here, we treat the Neumann and Dirichlet problems as well as the boundary value problem arising from acoustic scattering at the interface of two fluids. It achieves high accurac...

In this article we gain solvability to a nonlinear, second-order difference equation with discrete Neumann boundary conditions. Our methods involve new inequalities on the right-hand side of the difference equation and Schaefer’s theorem in the finitedimensional space setting. Running Head: Discrete BVPs AMS Subject Code: 39A12, 34B15 Corresponding Author: C C Tisdell

We will study a class of Steklov-Neumann boundary value problems for some quasilinear elliptic equations. We obtain result ensuring the existence of solutions when resonance and nonresonance conditions occur. The result was obtained by using variational arguments.

We consider second-order linear differential equations φ(x)y′′ + f(x)y′ + g(x)y = h(x) in the interval (−1, 1) with Dirichlet, Neumann or mixed Dirichlet-Neumann boundary conditions. We consider φ(x), f(x), g(x) and h(x) analytic in a Cassini disk with foci at x = ±1 containing the interval (−1, 1). The two-point Taylor expansion of the solution y(x) at the extreme points ±1 is used to give a c...

As a simpliied model for contact problems, we study a mixed Neumann-Robin boundary value problem for the Laplace operator in a smooth domain in R 2. The Robin condition contains a small parameter " inducing boundary layers of corner type at the transition points as proved in 4]. We present an integral equation for the numerical solution of this problem together with estimates of the error. We i...

due to high surface-to-volume ratio of nanoscale structures, surface stress effects have a significant influence on their behavior. in this paper, a two-dimensional problem for an elastic layer that is bonded to a rigid substrate and subjected to an inclined concentrated line load acting on the surface of the layer is investigated based on gurtin-murdoch continuum model to consider surface stre...

in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.