Existence and nonexistence of ground state solutions for quasilinear elliptic equations with a convection term

2012 ◽  
Vol 4 (1/2) ◽  
pp. 169
Author(s):  
Xiaoyan Cao ◽  
Zuodong Yang
Keyword(s):  
Ground State ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Convection Term ◽  
Ground State Solutions ◽  
Existence And Nonexistence ◽  
Quasilinear Elliptic

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

QUASILINEAR ELLIPTIC EQUATIONS WITH SINGULAR QUADRATIC GROWTH TERMS

2011 ◽  
Vol 13 (04) ◽  
pp. 607-642 ◽  
Author(s):  
LUCIO BOCCARDO ◽  
TOMMASO LEONORI ◽  
LUIGI ORSINA ◽  
FRANCESCO PETITTA
Keyword(s):  
Positive Solutions ◽  
Lebesgue Space ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Quadratic Growth ◽  
Open Set ◽  
Existence And Nonexistence ◽  
Nonexistence Of Solutions ◽  
Quasilinear Problems ◽  
Quasilinear Elliptic

In this paper, we deal with positive solutions for singular quasilinear problems whose model is [Formula: see text] where Ω is a bounded open set of ℝN, g ≥ 0 is a function in some Lebesgue space, and γ > 0. We prove both existence and nonexistence of solutions depending on the value of γ and on the size of g.

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 Multiple Solutions of Quasilinear Elliptic Equations in

2010 ◽  
Vol 2010 ◽  
pp. 1-12
Author(s):  
Huei-li Lin
Keyword(s):  
Elliptic Equation ◽  
Ground State ◽  
Elliptic Equations ◽  
Multiple Solutions ◽  
Quasilinear Elliptic Equation ◽  
Ground State Solution ◽  
The Other ◽  
Quasilinear Elliptic Equations ◽  
Positive Continuous Function ◽  
Quasilinear Elliptic

Assume that is a positive continuous function in and satisfies some suitable conditions. We prove that the quasilinear elliptic equation in admits at least two solutions in (one is a positive ground-state solution and the other is a sign-changing solution).

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