Ground State Solutions for A Quasilinear Elliptic Problem with a Convection Term

2012 ◽  
Vol 2 (2) ◽  
pp. 114-125
Author(s):  
Qin Li ◽  
Zuodong Yang
Keyword(s):  
Elliptic Problem ◽  
Ground State ◽  
Convection Term ◽  
Ground State Solutions ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic

Quasilinear elliptic problems with critical exponents and Hardy terms in ℝN

2010 ◽  
Vol 53 (1) ◽  
pp. 175-193 ◽  
Author(s):  
Dongsheng Kang
Keyword(s):  
Variational Methods ◽  
Elliptic Problem ◽  
Critical Exponents ◽  
Ground State ◽  
Elliptic Problems ◽  
Ground State Solutions ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

AbstractWe deal with a singular quasilinear elliptic problem, which involves critical Hardy-Sobolev exponents and multiple Hardy terms. Using variational methods and analytic techniques, the existence of ground state solutions to the problem is obtained.

Quasilinear elliptic problems with concave–convex nonlinearities

2017 ◽  
Vol 19 (06) ◽  
pp. 1650050 ◽  
Author(s):  
M. L. M. Carvalho ◽  
Edcarlos D. da Silva ◽  
C. Goulart
Keyword(s):  
Elliptic Problem ◽  
Ground State ◽  
Nonlinear Term ◽  
Laplacian Operator ◽  
Main Difficulty ◽  
Quasilinear Elliptic Problem ◽  
Existence And Multiplicity ◽  
Quasilinear Elliptic Problems ◽  
Nehari Method ◽  
Quasilinear Elliptic

In this paper, the existence and multiplicity of solutions for a quasilinear elliptic problem driven by the [Formula: see text]-Laplacian operator is established. These solutions are also built as ground state solutions using the Nehari method. The main difficulty arises from the fact that the [Formula: see text]-Laplacian operator is not homogeneous and the nonlinear term is indefinite.

MULTIPLE POSITIVE SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS ASSOCIATED TO A CLASS OF p-LAPLACIAN LIKE OPERATORS

2003 ◽  
Vol 05 (05) ◽  
pp. 737-759 ◽  
Author(s):  
NOBUYOSHI FUKAGAI ◽  
KIMIAKI NARUKAWA
Keyword(s):  
Positive Solutions ◽  
Elliptic Problem ◽  
Eigenvalue Problems ◽  
Multiple Positive Solutions ◽  
Combined Effects ◽  
Nonlinear Eigenvalue Problems ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic ◽  
Nonlinear Eigenvalue

This paper deals with positive solutions of a class of nonlinear eigenvalue problems. For a quasilinear elliptic problem (#) - div (ϕ(|∇u|)∇u) = λf(x,u) in Ω, u = 0 on ∂Ω, we assume asymptotic conditions on ϕ and f such as ϕ(t) ~ tp0-2, f(x,t) ~ tq0-1as t → +0 and ϕ(t) ~ tp1-2, f(x,t) ~ tq1-1as t → ∞. The combined effects of sub-nonlinearity (p0> q0) and super-nonlinearity (p1< q1) with the subcritical term f(x,u) imply the existence of at least two positive solutions of (#) for 0 < λ < Λ.

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