Electron. J. Differential Equations, Vol. 2019 (2019), No. 36, pp. 1-9.

Nonlinear Fredholm equations in modular function spaces

Mostafa Bachar

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 5, 2019.
Math Subject Classifications: 46A80, 47H10, 45G05.
Key Words: Electrorheological fluids; fixed point; Fredholm equations; modular function spaces; variable exponent spaces.

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Mostafa Bachar
College of Sciences
Department of Mathematics
King Saud University
Riyadh, Saudi Arabia
email: mbachar@ksu.edu.sa

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