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

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
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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: http://hdl.handle.net/20.500.11769/365598
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 18
  • ???jsp.display-item.citation.isi??? 19
social impact