Singular nonhomogeneous quasilinear elliptic equations with a convection term

2017 ◽  
Vol 290 (14-15) ◽  
pp. 2280-2295
Author(s):  
J. V. Gonçalves ◽  
M. R. Marcial ◽  
O. H. Miyagaki
Keyword(s):  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Convection Term ◽  
Quasilinear Elliptic

scholarly journals Double phase problems with variable growth and convection for the Baouendi–Grushin operator

2020 ◽  
Vol 71 (6) ◽  
Author(s):  
Anouar Bahrouni ◽  
Vicenţiu D. Rădulescu ◽  
Patrick Winkert
Keyword(s):  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Stationary Waves ◽  
Convection Term ◽  
Pseudomonotone Operators ◽  
Qualitative Properties ◽  
Transonic Flows ◽  
Grushin Operator ◽  
Double Phase ◽  
Quasilinear Elliptic

AbstractIn this paper we study a class of quasilinear elliptic equations with double phase energy and reaction term depending on the gradient. The main feature is that the associated functional is driven by the Baouendi–Grushin operator with variable coefficient. This partial differential equation is of mixed type and possesses both elliptic and hyperbolic regions. We first establish some new qualitative properties of a differential operator introduced recently by Bahrouni et al. (Nonlinearity 32(7):2481–2495, 2019). Next, under quite general assumptions on the convection term, we prove the existence of stationary waves by applying the theory of pseudomonotone operators. The analysis carried out in this paper is motivated by patterns arising in the theory of transonic flows.

scholarly journals Quasilinear Dirichlet Problems with Degenerated p-Laplacian and Convection Term

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 139
Author(s):  
Dumitru Motreanu ◽  
Elisabetta Tornatore
Keyword(s):  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Convection Term ◽  
Bounded Solutions ◽  
Dirichlet Problems ◽  
Abstract Result ◽  
Functional Setting ◽  
Quasilinear Elliptic ◽  
Substantial Change

The paper develops a sub-supersolution approach for quasilinear elliptic equations driven by degenerated p-Laplacian and containing a convection term. The presence of the degenerated operator forces a substantial change to the functional setting of previous works. The existence and location of solutions through a sub-supersolution is established. The abstract result is applied to find nontrivial, nonnegative and bounded solutions.

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