On Solutions of Quadratic Integral Equations in Orlicz Spaces

On Quadratic Integral Equations of Urysohn Type in Fréchet Spaces

0 u(t, s, x(s)) ds, t ∈ J := [0,+∞), where f : J → R, u : J × [0, T ] × R → R are given functions and A : C(J,R) → C(J,R) is an appropriate operator. Here C(J,R) denotes the space of continuous functions x : J → R. Integral equations arise naturally from many applications in describing numerous real world problems, see, for instance, books by Agarwal et al. [1], Agarwal and O’Regan [2], Cordune...

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces

Existence of solutions of infinite systems of integral equations in the Frechet spaces

In this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the Fr´echet spaces. Our aim is to provide a few generalization of Tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of Tych...

Existence of Solutions for Elliptic Equations Having Natural Growth Terms in Orlicz Spaces

and which satisfies the classical sign condition g(x,s,ξ)s ≥ 0. The right-hand side f is assumed to belong to W−1EM(Ω). It is well known that Gossez [12] solved (1.1) in the case where g depends only on x and u. If g depends also on ∇u, existence theorems have recently been proved by Benkirane and Elmahi in [3, 4] by making some restrictions. In [3], g is supposed to satisfy a “nonnatural” grow...

On the Solutions of Quadratic Diophantine Equations

We determine a finite set of representatives of the set of local solutions in a maximal lattice modulo the stabilizer of the lattice in question for a quadratic Diophantine equation. Our study is based on the works of Shimura on quadratic forms, especially [AQC] and [IQD]. Indeed, as an application of the result, we present a criterion (in both global and local cases) of the maximality of the l...