On 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...

Asymptotic Behaviour of Some Equations in Orlicz Spaces

In this paper, we prove an existence and uniqueness result for solutions of some bilateral problems of the form  〈Au, v − u〉 ≥ 〈f, v − u〉, ∀v ∈ K u ∈ K where A is a standard Leray-Lions operator defined on W 1 0 LM (Ω), with M an N-function which satisfies the ∆2-condition, and where K is a convex subset of W 1 0 LM (Ω) with obstacles depending on some Carathéodory function g(x, u). We consid...

Quadratic Integral Equations in Reflexive Banach Space

This paper is devoted to proving the existence of weak solutions to some quadratic integral equations of fractional type in a reflexive Banach space relative to the weak topology. A special case will be considered.

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces

Modular Estimates in Orlicz Spaces and Hammerstein Operator Equations

1. Let us recall the basic definitions of the theory of Orlicz spaces (see, for example, [1]). Henceforth (Ω,A, μ) is the triple consisting of a set Ω, σ-algebra A of its subsets and a σ-additive measure μ defined on A. It is assumed that μ is continuous on Ω (that is any set of positive measure can be divided into two sets of equal measures) and is finite: μ(Ω) < ∞. Let M : [0,+∞) → [0,+∞) be ...