Existence results for a quasilinear elliptic problem with a gradient term via shooting method

2011 ◽  
Vol 218 (8) ◽  
pp. 4161-4168 ◽  
Author(s):  
Dragos-Patru Covei
Keyword(s):  
Elliptic Problem ◽  
Shooting Method ◽  
Existence Results ◽  
Gradient Term ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic

scholarly journals Existence Results for a Class of the Quasilinear Elliptic Equations with the Logarithmic Nonlinearity

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Zhoujin Cui ◽  
Zisen Mao ◽  
Wen Zong ◽  
Xiaorong Zhang ◽  
Zuodong Yang
Keyword(s):  
Elliptic Problem ◽  
Elliptic Equations ◽  
Nehari Manifold ◽  
Existence Results ◽  
Quasilinear Elliptic Equations ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic

In this paper, the nonlinear quasilinear elliptic problem with the logarithmic nonlinearity − div ∇ u p − 2 ∇ u = a x φ p u log u + h x ψ p u in Ω ⊂ R n was studied. By means of a double perturbation argument and Nehari manifold, the authors obtain the existence results.

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.

scholarly journals Existence of W01,1Ω Solutions to Non-Coercivity Quasilinear Elliptic Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Jimao Xiawu ◽  
Shuibo Huang ◽  
Yingyuan Mi ◽  
Maoji Ri
Keyword(s):  
Elliptic Problem ◽  
Bounded Subset ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic ◽  
Open Bounded Subset

In this paper we consider the existence of W01,1Ω solutions to following kind of problems −div∇up−2∇u/1+uθp−1=fx,x∈Ω;ux=0,x∈∂Ω where Ω is an open bounded subset of RNN>2, maxp−2N+1/p−1N−1,0<θ<1 and 1<p⩽1+N−1/N1−θ+θ, f is a function which belongs to a suitable integrable space.

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