Existence results for nonlinear Fourier problems with variable exponent growth
DOI: https://doi.org/10.3846/mma.2026.25157Abstract
We study nonlinear problems which use the generalized $\alpha(x)-$Laplacian operator under Fourier boundary conditions with $L^{1}$ data. Our research establishes both weak and entropy solutions through the framework of variable exponent Sobolev spaces. Our solution method uses monotone operator theory and appropriate approximation methods to develop a unified approach for dealing with nonlinearities that exhibit variable growth. These findings help expand knowledge about nonlinear Fourier-type problems while demonstrating how entropy formulations enable well-posedness for problems with minimal data requirements.
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Lebesgue and Sobolev spaces with variable exponent, Fourier boundary conditions, weak solutions, entropy solution, nonlinear elliptic problemsHow to Cite
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Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University.
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