Nonlinear Elliptic Problem Involving Natural Growth Term, Measure Data, Variable Exponent and Neumann Boundary Conditions

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Résumé

In this paper, we investigate the existence of solutions to an elliptic problem with natural growth term, diffuse measure data and Neumann boundary conditions. Using approxi- mation methods via Yosida regularization and truncation, along with maximal monotone operator methods in Banach spaces, we prove the existence of a renormalized solution. We further describe how our notion of solution relates to the entropy solution framework.

Mots-clés

Generalized Lebesgue-Sobolev spaces · Sobolev spaces · Leray-Lions operator · Truncations · Maximal monotone graph · Entropy solution · Marcinkiewicz spaces