On a Class of Nonlinear Elliptic Equations with General Growth in the Gradient

M. Francesca Betta, Anna Mercaldo () and Roberta Volpicelli
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M. Francesca Betta: Dipartimento di Ingegneria, Università di Napoli Parthenope, Centro Direzionale, Isola C4, 80143 Napoli, Italy
Anna Mercaldo: Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Complesso Monte S. Angelo, Via Cintia, 80126 Napoli, Italy
Roberta Volpicelli: Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Complesso Monte S. Angelo, Via Cintia, 80126 Napoli, Italy

Mathematics, 2024, vol. 12, issue 3, 1-15

Abstract: In this paper, we prove an existence and uniqueness result for a class of Dirichlet boundary value problems whose model is − Δ p u = β | ∇ u | q + c | u | p − 2 u + f in Ω , u = 0 on ∂ Ω , where Ω is an open bounded subset of R N , N ≥ 2 , 1 < p < N , Δ p u is the so-called p -Laplace operator, and p − 1 < q < p . We assume that β is a positive constant, c and f are measurable functions belonging to suitable Lorentz spaces. Our approach is based on Schauder fixed point theorem.

Keywords: existence; uniqueness; nonlinear elliptic equations; fixed point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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