Nonlinear Fredholm equations in modular function spaces

Abstract

<p>We investigate the existence of solutions in modular function spaces of the Fredholm integral equation</p> <p>Φ(θ) = g(θ) + ∫¹₀ ƒ(θ, σ, Φ(σ)) dσ,</pre> <p>where Φ(θ), g(θ) ∈ L_ρ, θ ∈ [0, 1], ƒ : [0, 1] x [0, 1] x L_ρ → ℝ. An application in the variable exponent Lebesgue spaces is derived under minimal assumptions on the problem data.</p>