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This analysis demonstrates solutions' existence in nonlinear elliptic systems, implying mathematical robustness in various scenarios.
We consider the nonlinear elliptic system where is a bounded, open subset of ; is a coercive, symmetric matrix with coefficients; ; for or ; and depends on the summability of . Using a duality technique, we prove the existence of solutions in the following cases for both expressions of : 1. If , then for and for some . 2. If , then . 3. If , , then .
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Boccardo et al. (2025) studied this question.
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