We state sufficient conditions for the existence of positive bounded, almost automorphic or almost periodic solutions of the following nonlinear infinite delay integral equation:

We present computational results using CORAL, a parallel, three-dimensional, nonlinear magnetostatic code based on a volume integral equation formulation. A key feature of CORAL is the ability to solve, in parallel, the large, dense systems of linear equations that are inherent in the use of integral equation methods. Using the Chameleon and PSLES libraries ensures portability and access to the...

This paper develops a method for solving for the dynamic general equilibrium of a deterministic continuous time overlapping generations model with a finite-horizon life-cycle. The model has isoelastic preferences and allows for general assumptions about individual endowments and demographics. Solving for an equilibrium reduces to solving a nonlinear integral equation. In the special case of log...

We prove a generalization of a measure theoretic fixed point theorem of Darbo in Banach spaces which includes some well-known fixed point theorems of Dhage and Sadovskii as special cases. A generalized nonlinear functional integral equation is studied via Dhage fixed point theorem for attractivity of the solutions on unbounded intervals of real line. Finally the validity of our hypotheses impos...

We discuss an integral form of the Cauchy initial value problem for the nonlinear Schrödinger equation with variable coefficients. Some special and limiting cases are outlined.

in this paper we investigate the existence and uniqueness for volterra-fredholm type integral equations and extension of this type of integral equations. the result is obtained by using the  coupled fixed point theorems in the framework of banach space $ x=c([a,b],mathbb{r})$. finally, we  give an example to illustrate the applications of our results.

This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form: { D t x(t) = f(t, x(t), D β t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = ∫ 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle. Keywords—Fractional differential equation; Integral boundary condi...

A linearizing integral transform is proposed which relates solutions of a spectral problem associated with a class of inte-grable partial difference equations to any given solution of the spectral problem. Examples of this class are lattice versions of the isotropic Heisenberg spin chain, the nonlinear SchrSdinger equation and the (complex) sine-Gordon equation. 1. Introduction. Recently a dire...

Nonlinear evolution equations are widely used to describe complex phenomena in various sciences such as fluid physics, condensed matter, biophysics, plasma physics, nonlinear optics, quantum field theory and particle physics, etc. In recent years, various powerful methods have been presented for finding exact solutions of the nonlinear evolution equations in mathematical physics, such as, tanh ...

In the recent years, a new attention has been given to reaction-diffusion systems which involve an integral over the spatial domain of a function of the desired solution on the boundary conditions; see [2, 5, 7, 6, 9, 10, 17, 18, 19, 20, 22] and the references cited therein. Most of the studied problems in the current literature are devoted to problems which combine a classical boundary conditi...