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

Author

Listed:
  • 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)

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.

Suggested Citation

  • M. Francesca Betta & Anna Mercaldo & Roberta Volpicelli, 2024. "On a Class of Nonlinear Elliptic Equations with General Growth in the Gradient," Mathematics, MDPI, vol. 12(3), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:409-:d:1327453
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