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 providedFile in questo prodotto:
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