scholarly journals Local behavior of positive solutions to a nonlinear biharmonic equation near isolated singularities

2022 ◽  
Vol 214 ◽  
pp. 112594
Author(s):  
Ke Wu
Keyword(s):  
Positive Solutions ◽  
Biharmonic Equation ◽  
Local Behavior ◽  
Isolated Singularities

Uniqueness theorem for the entire positive solutions of biharmonic equations in Rn

2000 ◽  
Vol 130 (3) ◽  
pp. 651-670 ◽  
Author(s):  
X. Xu
Keyword(s):  
Uniqueness Theorem ◽  
Positive Solutions ◽  
Biharmonic Equation ◽  
Negative Solution ◽  
Biharmonic Equations ◽  
Conformally Invariant ◽  
Moving Spheres

The entire positive solutions of a conformally invariant biharmonic equation in Rn will be classified using the method of moving spheres. As a byproduct, one also shows that any entire non-negative solution of the equation Δ2u = up with 1 ≤ p < (n + 4)/(n−4) with n ≥ 2 is zero.

scholarly journals Isolated singularities of positive solutions for Choquard equations in sublinear case

2018 ◽  
Vol 20 (04) ◽  
pp. 1750040 ◽  
Author(s):  
Huyuan Chen ◽  
Feng Zhou
Keyword(s):  
Positive Solutions ◽  
Riesz Potential ◽  
Singular Solutions ◽  
Nonlocal Term ◽  
Choquard Equation ◽  
Qualitative Properties ◽  
Isolated Singularities ◽  
Nonexistence And Existence

Our purpose of this paper is to study the isolated singularities of positive solutions to Choquard equation in the sublinear case [Formula: see text] [Formula: see text] where [Formula: see text] and [Formula: see text] is the Riesz potential, which appears as a nonlocal term in the equation. We investigate the nonexistence and existence of isolated singular solutions of Choquard equation under different range of the pair of exponent [Formula: see text]. Furthermore, we obtain qualitative properties for the minimal singular solutions of the equation.

Symmetry of Positive Solutions to the Coupled Fractional System with Isolated Singularities

2021 ◽  
Vol 37 (9) ◽  
pp. 1437-1452
Author(s):  
Meng Hui Li ◽  
Jin Chun He ◽  
Hao Yuan Xu ◽  
Mei Hua Yang
Keyword(s):  
Positive Solutions ◽  
Isolated Singularities ◽  
Fractional System
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