On a quasilinear elliptic problem with convection term and nonlinear boundary condition. (October 2019)

• Record Type: Journal Article
• Authors: Marano, Salvatore A.; Winkert, Patrick
• Is Part Of: Nonlinear analysis. Volume 187(2019)
• Page Start: 159
• Page End: 169
• Publication Date: 2019-10
• Subjects: 35J15 -- 35J62; Quasilinear elliptic equations -- Convection term -- Nonlinear boundary condition -- Uniqueness -- Asymptotic behavior; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.04.008
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The first part of this paper deals with existence of solutions to the quasilinear elliptic problem (P) − div a ( x, ∇ u ) = f ( x, u, ∇ u ) in Ω, a ( x, ∇ u ) ⋅ ν = g ( x, u ) − ζ | u | p − 2 u on ∂ Ω, involving a general nonhomogeneous differential operator, namely div a, and Carathéodory functions f : Ω × R × R N → 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.