Nonexistence of solutions of the dirichlet problem for some quasilinear elliptic equations in a half-space

2016 ◽  
Vol 52 (6) ◽  
pp. 749-760
Author(s):  
E. I. Galakhov ◽  
O. A. Salieva
Keyword(s):  
Dirichlet Problem ◽  
Half Space ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Nonexistence Of Solutions ◽  
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 Existence of Renormalized Solutions for Some Anisotropic Quasilinear Elliptic Equations

2020 ◽  
Vol 44 (4) ◽  
pp. 617-637
Author(s):  
T. AHMEDATT ◽  
A. AHMED ◽  
H. HJIAJ ◽  
A. TOUZANI
Keyword(s):  
Dirichlet Problem ◽  
Growth Condition ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Renormalized Solutions ◽  
Carathéodory Function ◽  
Regularity Results ◽  
Quasilinear Elliptic

In this paper, we consider a class of anisotropic quasilinear elliptic equations of the type ( | ∑N { − ∂ia (x, u, ∇u ) + |u|s(x )− 1u = f (x,u ), in Ω, i |( i=1 u = 0 on ∂ Ω, where f(x,s) is a Carathéodory function which satisfies some growth condition. We prove the existence of renormalized solutions for our Dirichlet problem, and some regularity results are concluded.

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