The Integral Representation of the Positive Solutions of the Generalized Weinstein Equation on a Quarter-Space

1988 ◽  
Vol 19 (6) ◽  
pp. 1348-1354 ◽  
Author(s):  
Ömer Akin
Keyword(s):  
Integral Representation ◽  
Positive Solutions ◽  
Weinstein Equation ◽  
Quarter Space

scholarly journals Monotonicity of Harnack Inequality for Positive Invariant Harmonic Functions

2007 ◽  
Vol 2007 ◽  
pp. 1-12
Author(s):  
Yifei Pan ◽  
Mei Wang
Keyword(s):  
Positive Solutions ◽  
Harnack Inequality ◽  
Harmonic Functions ◽  
Monotonicity Property ◽  
Weinstein Equation ◽  
Refined Estimate

A monotonicity property and a refined estimate of Harnack inequality are derived for positive solutions of the Weinstein equation.

Positive solutions for a quasilinear system Via blow up

1993 ◽  
Vol 18 (12) ◽  
pp. 2071-2106
Author(s):  
Philippe Clément ◽  
Raúl Manásevich ◽  
Enzo Mitidieri
Keyword(s):  
Positive Solutions ◽  
Blow Up ◽  
Quasilinear System

On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value

2006 ◽  
Vol 11 (4) ◽  
pp. 323-329 ◽  
Author(s):  
G. A. Afrouzi ◽  
S. H. Rasouli
Keyword(s):  
Boundary Value Problems ◽  
Positive Solution ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Smooth Bounded Domain ◽  
Elliptic Boundary Value ◽  
Existence Of Positive Solutions

This study concerns the existence of positive solutions to classes of boundary value problems of the form−∆u = g(x,u), x ∈ Ω,u(x) = 0, x ∈ ∂Ω,where ∆ denote the Laplacian operator, Ω is a smooth bounded domain in RN (N ≥ 2) with ∂Ω of class C2, and connected, and g(x, 0) < 0 for some x ∈ Ω (semipositone problems). By using the method of sub-super solutions we prove the existence of positive solution to special types of g(x,u).

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