scholarly journals A nondegeneracy condition for a semilinear elliptic system and the existence of 1- bump solutions

2019 ◽  
Vol 39 (12) ◽  
pp. 6995-7012 ◽  
Author(s):  
Piero Montecchiari ◽  
◽  
Paul H. Rabinowitz ◽  
Keyword(s):  
Elliptic System ◽  
Nondegeneracy Condition ◽  
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].

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