On a quasilinear elliptic problem with convection term and nonlinear boundary condition. (October 2019) - Marano, Salvatore A.; Winkert, Patrick
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.