scholarly journals Positive solutions for nonlinear singular elliptic equations of p-Laplacian type with dependence on the gradient

2019 ◽  
Vol 58 (1) ◽  
Author(s):  
Zhenhai Liu ◽  
Dumitru Motreanu ◽  
Shengda Zeng
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Singular Elliptic Equations

Multiple positive solutions for singular elliptic equations with weighted Hardy terms and critical Sobolev–Hardy exponents

2010 ◽  
Vol 140 (3) ◽  
pp. 617-633 ◽  
Author(s):  
Tsing-San Hsu ◽  
Huei-Li Lin
Keyword(s):  
Elliptic Equation ◽  
Variational Methods ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Smooth Boundary ◽  
Continuous Functions ◽  
Multiple Positive Solutions ◽  
Singular Elliptic Equations ◽  
Multiplicity Of Positive Solutions ◽  
Image Position

Variational methods are used to prove the multiplicity of positive solutions for the following singular elliptic equation:where 0 ∈ Ω ⊂ ℝN, N ≥ 3, is a bounded domain with smooth boundary ∂ Ω, λ > 0 , $1\le q<2$, $0\le\mu<\bar{\mu}=(N-2)^2/4$, 0 ≤ s < 2, 2*(s)=2(N−s)/(N−2) and f and g are continuous functions on $\bar{\varOmega}$, that change sign on Ω.

scholarly journals Existence of a positive solution for a singular system

2010 ◽  
Vol 140 (2) ◽  
pp. 435-447 ◽  
Author(s):  
Marcelo Montenegro ◽  
Antonio Suárez
Keyword(s):  
Boundary Condition ◽  
Positive Solution ◽  
Positive Solutions ◽  
Dirichlet Boundary Condition ◽  
Elliptic Equations ◽  
Dirichlet Boundary ◽  
Singular System ◽  
Singular Elliptic Equations ◽  
Existence Of Positive Solutions

We show the existence and non-existence of positive solutions to a system of singular elliptic equations with the Dirichlet boundary condition.

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