In this paper we introduce an approach via optimization methods to find approximate solutions for nonlinear Fredholm integral equations of the first kind. To this purpose, we consider two stages of approximation. First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems and optimal ...

This work is devoted to study the existence and the regularity of solutions of two nonlinear problems of fourth order governed by p-biharmonic operators in nonresonance cases. In the first problem we establish the nonresonance part of the Fredholm alternative. In the second problem, nonresonance relative to the first eigenvalue is considered for p = 2 at the case where the nonresonance is betwe...

In some recent papers, a method was developed of reducing coupled fixed point problems in (ordered) metric and various generalized metric spaces to the respective results for mappings with one variable. In this paper, we apply the mentioned method and obtain some coupled fixed point results for mappings satisfying φ-weak contractive conditions in ordered b-metric spaces. Examples show how these...

1. Elliptic Differential Operators 1 1.1. Partial differential operators 1 1.2. Sobolev spaces and Hölder spaces 10 1.3. Apriori estimates and elliptic regularity 20 1.4. Elliptic operators on compact manifolds 28 2. Non-linear Elliptic Equations 35 2.1. Banach manifolds and Fredholm operators 35 2.2. Moduli space of nonlinear elliptic equations 39 2.3. The Sard-Smale theorem and transversality...

In this paper, we present a method for calculated the numerical approximation of nonlinear Fredholm Volterra Hammerstein integral equation, which uses the properties of rationalized Haar wavelets. The main tool for error analysis is the Banach fixed point theorem. An upper bound for the error was obtained and the order of convergence is analyzed. An algorithm is presented to compute and illustr...

In this paper we study spectra and Fredholm properties of Ornstein-Uhlenbeck operators Lv(x) := A4v(x) + 〈Sx,∇v(x)〉+Df(v?(x))v(x), x ∈ R, d > 2, where v? : R → R is the profile of a rotating wave satisfying v?(x) → v∞ ∈ R as |x| → ∞, the map f : R → R is smooth, the matrix A ∈ R has eigenvalues with positive real parts and commutes with the limit matrix Df(v∞). The matrix S ∈ R is assumed to be...

In this paper, an iterative method of successive approximations to the approximate solution nonlinear Hammerstein-Fredholm integral equations using optimal quadrature formula for classes functions Lipschitz types is provided. Also, convergence analysis and numerical stability proposed are proved. Finally, some examples verify theoretical results show accuracy method.