scholarly journals The perturbation method for the skew-symmetric strongly elliptic systems of PDEs

2021 ◽  
pp. 1-10
Author(s):  
A.O. Bagapsh
Keyword(s):  
Perturbation Method ◽  
Elliptic Systems ◽  
Systems Of Pdes

scholarly journals Symmetry results for stable and monotone solutions to fibered systems of PDEs

2015 ◽  
Vol 17 (04) ◽  
pp. 1450035 ◽  
Author(s):  
Serena Dipierro ◽  
Andrea Pinamonti
Keyword(s):  
Elliptic Systems ◽  
Type Formula ◽  
Symmetry Properties ◽  
Systems Of Pdes ◽  
Symmetry Result ◽  
Monotone Solutions

We study the symmetry properties for solutions of elliptic systems of the type [Formula: see text] where x ∈ ℝm with 1 ≤ m < N, X = (x, y) ∈ ℝm × ℝN-m, and F1,…,Fn are the derivatives with respect to ξ1,…,ξn of some F = F(x,ξ1,…,ξn) such that for any i = 1,…,n and any fixed (x,ξ1,…,ξi-1,ξi+1,…,ξn) ∈ ℝm × ℝn-1 the map ξi → F(x,ξ1,…,ξi,…,ξn) belongs to C2(ℝ). We obtain a Poincaré-type formula for the solutions of the system and we use it to prove a symmetry result both for stable and for monotone solutions.

Infinitely Many Sign-changing Solutions for Quasilinear Elliptic Systems in ℝN

2015 ◽  
Vol 15 (4) ◽  
Author(s):  
Wei Zhang ◽  
Xiangqing Liu
Keyword(s):  
Perturbation Method ◽  
Elliptic Systems ◽  
Invariant Sets ◽  
Quasilinear Elliptic Systems ◽  
Sign Changing Solutions ◽  
Quasilinear Elliptic

AbstractIn this paper, by using a perturbation method together with the method of invariant sets of descending flow, we obtain the existence of infinitely many sign-changing solutions of quasilinear elliptic systems in ℝ

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