scholarly journals Semilinear elliptic system with boundary singularity

2020 ◽  
Vol 40 (4) ◽  
pp. 2189-2212
Author(s):  
Yimei Li ◽  
◽  
Jiguang Bao
Keyword(s):  
Elliptic System ◽  
Boundary Singularity ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic System

NON-EXISTENCE, MONOTONICITY FOR POSITIVE SOLUTIONS OF SEMILINEAR ELLIPTIC SYSTEM IN $\mathbb{R}_+^N$

2010 ◽  
Vol 12 (03) ◽  
pp. 351-372 ◽  
Author(s):  
YUXIA GUO
Keyword(s):  
Weak Solution ◽  
Elliptic System ◽  
Half Space ◽  
Positive Solutions ◽  
Integral Inequality ◽  
Existence Results ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic System ◽  
Moving Plane ◽  
Positive Weak Solution

In this paper, by using the Alexandrov–Serrin method of moving plane combined with integral inequality, we prove some non-existence results for positive weak solution of semilinear elliptic system in the half-space [Formula: see text].

Positive solutions for some competitive elliptic systems

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Ramzi Alsaedi ◽  
Habib Mâagli ◽  
Noureddine Zeddini
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Elliptic System ◽  
Elliptic Systems ◽  
Global Behavior ◽  
Continuous Solutions ◽  
Kato Class ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic System ◽  
Compact Boundary

AbstractUsing some potential theory tools and the Schauder fixed point theorem, we prove the existence of positive bounded continuous solutions with a precise global behavior for the semilinear elliptic system Δu = p(x)u α ν r in domains D of ℝn, n ≥ 3, with compact boundary (bounded or unbounded) subject to some Dirichlet conditions, where α ≥ 1, β ≥ 1, r ≥ 0, s ≥ 0 and the potentials p, q are nonnegative and belong to the Kato class K(D).

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