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Analysis establishes weak solution for nonlocal thermistor problem using Sobolev spaces, indicating key theoretical findings.
The focus of this paper, is to establish the existence of a weak solution for a problem that involves p(x)-Laplacian. We achieve this by utilizing the topological degree theory, which is based on a class of demi-continuous operators of generalized (S+) type, as presented in [6], in conjunction with the theory of variable-exponent Sobolev spaces. Additionally, we provide a numerical example to verify and validate the theoretical results.
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Dahi et al. (2025) studied this question.
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