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

Positive solutions for a weighted fractional system

2018 ◽  
Vol 38 (3) ◽  
pp. 935-949 ◽  
Author(s):  
Pengyan WANG ◽  
Yongzhong WANG
Keyword(s):  
Positive Solutions ◽  
Fractional System

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.

scholarly journals A Sum Operator Method for the Existence and Uniqueness of Positive Solutions to a System of Nonlinear Fractional Integral Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Jing Wu ◽  
Tunhua Wu
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Iterative Scheme ◽  
Operator Method ◽  
Quadratic System ◽  
System Of Integral Equations ◽  
Fractional System

This paper is concerned with the existence and uniqueness of positive solutions for a Volterra nonlinear fractional system of integral equations. Our analysis relies on a fixed point theorem of a sum operator. The conditions for the existence and uniqueness of a positive solution to the system are established. Moreover, an iterative scheme is constructed for approximating the solution. The case of quadratic system of fractional integral equations is also considered.

Singular semilinear elliptic inequalities in the exterior of a compact set

2013 ◽  
Vol 143 (3) ◽  
pp. 563-588 ◽  
Author(s):  
Marius Ghergu ◽  
Steven D. Taliaferro
Keyword(s):  
Positive Solutions ◽  
Continuous Functions ◽  
Minimal Solution ◽  
Compact Set ◽  
Optimal Conditions ◽  
Isolated Singularities ◽  
Semilinear Elliptic ◽  
Elliptic Inequality ◽  
Isolated Point ◽  
Elliptic Inequalities

We study the semilinear elliptic inequality –Δu ≥ φ(δK (x))f(u) in ℝN / K, where φ, f are positive and non-increasing continuous functions. Here K ⊂ ℝN (N ≥ 3) is a compact set with finitely many components, each of which is either the closure of a C2 domain or an isolated point, and δK (x) = dist(x, ∂K). We obtain optimal conditions in terms of φ and f for the existence of C2-positive solutions. Under these conditions we prove the existence of a minimal solution and we investigate its behaviour around ∂K as well as the removability of the (possible) isolated singularities.

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