Extreme solutions of nonlinear, second order integro-differential equations in Banach spaces.
The general theory of factorial analysis of continuous correspondance (FACC) is used to investigate the binary case of a continuous probability measure defined as:T(x,y) = ayn + b, (x,y) ∈ D & n ∈ N = 0, elsewhereWhere n ≥ 0, a and b are the parameters of this distribution, while the domain D is a variable trapezoidal inscribed in the unit square. The trapezoid depends on two parameters α and β.This problem is solved. As special cases of our problem we obtain a complete solution for...
We present, in a uniform manner, several integral equations of the first kind for the solution of the two-dimensional interior Dirichlet boundary value problem. We apply a general numerical collocation method to the various equations, and thereby we compare the various integral equations, and recommend two of them. We give a survey of the various numerical methods, and present a simple method for the numerical solution of the recommended integral equations.
In this paper we prove some fixed point theorems of the Banach and Krasnosel’skii type for mappings on the -tuple Cartesian product of a Banach algebra over . Using these theorems existence results for a system of integral equations of the Gripenberg’s type are proved. A sufficient condition for the nonexistence of blowing-up solutions of this system of integral equations is also proved.