The first part of this paper deals with existence of solutions to the quasilinear elliptic problem − div a(x, ∇u) = f(x, u, ∇u) in Ω, a(x, ∇u) · ν = g(x, u) − ζ|u| p−2u on ∂Ω, (P) involving a general nonhomogeneous differential operator, namely div a, and Carathéodory functions f : Ω×R×RN → R and g : ∂Ω×R → R. Under appropriate conditions on the perturbations, we show that (P) possesses a bounded solution. In the second part, we consider the special case when div a is the (p, q)-Laplacian with a parameter µ > 0, and study the asymptotic behavior of solutions as µ goes to zero or to infinity. A uniqueness result is also provided

On a quasilinear elliptic problem with convection term and nonlinear boundary condition

S. A. Marano;
2019-01-01

Abstract

The first part of this paper deals with existence of solutions to the quasilinear elliptic problem − div a(x, ∇u) = f(x, u, ∇u) in Ω, a(x, ∇u) · ν = g(x, u) − ζ|u| p−2u on ∂Ω, (P) involving a general nonhomogeneous differential operator, namely div a, and Carathéodory functions f : Ω×R×RN → R and g : ∂Ω×R → R. Under appropriate conditions on the perturbations, we show that (P) possesses a bounded solution. In the second part, we consider the special case when div a is the (p, q)-Laplacian with a parameter µ > 0, and study the asymptotic behavior of solutions as µ goes to zero or to infinity. A uniqueness result is also provided
2019
Quasilinear elliptic equations; Convection term; Nonlinear boundary condition; Uniqueness; Asymptotic behavior.
File in questo prodotto:
File Dimensione Formato  
1-s2.0-S0362546X19301294-main.pdf

solo gestori archivio

Tipologia: Documento in Post-print
Licenza: Creative commons
Dimensione 715.31 kB
Formato Adobe PDF
715.31 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/365598
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 33
  • ???jsp.display-item.citation.isi??? 33
social impact