Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 36, pp. 1-9.

Title: Nonlinear Fredholm equations in modular function spaces

Author: Mostafa Bachar (King Saud Univ., Riyadh, Saudi Arabia)

Abstract:
 We investigate the existence of solutions in modular function spaces
 of the Fredholm integral equation
 $$
 \Phi(\theta) = g(\theta) + \int^1_0 f(\theta,\sigma, \Phi(\sigma)) \,d\sigma,
 $$
 where $\Phi(\theta), g(\theta)\in L_{\rho}, \theta\in [0,1],
 f: [0,1]\times[0,1]\times L_{\rho}\to \mathbb{R}$.
 An application in the variable exponent Lebesgue spaces is
 derived under minimal assumptions on the problem data.

Submitted March 13, 2018. Published March 05, 2019.
Math Subject Classifications: 46A80, 47H10, 45G05.
Key Words: Electrorheological fluids; fixed point; Fredholm equations;
           modular function spaces; variable exponent spaces.