scholarly journals Multiplicity of nodal solutions to the Yamabe problem

2017 ◽  
Vol 56 (5) ◽  
Author(s):  
Mónica Clapp ◽  
Juan Carlos Fernández
Keyword(s):  
Yamabe Problem ◽  
Nodal Solutions

scholarly journals Nodal solutions for the fractional Yamabe problem on Heisenberg groups

2019 ◽  
Vol 150 (2) ◽  
pp. 771-788 ◽  
Author(s):  
Alexandru Kristály
Keyword(s):  
Weak Solutions ◽  
Unitary Group ◽  
Original Problem ◽  
Laplacian Operator ◽  
Yamabe Problem ◽  
Heisenberg Groups ◽  
Nodal Solutions ◽  
Compactness Result ◽  
Homogeneous Dimension ◽  
Nodal Properties

AbstractWe prove that the fractional Yamabe equation ${\rm {\cal L}}_\gamma u = \vert u \vert ^{((4\gamma )/(Q-2\gamma ))}u$ on the Heisenberg group ℍn has [n + 1/2] sequences of nodal (sign-changing) weak solutions whose elements have mutually different nodal properties, where ${\rm {\cal L}}_\gamma $ denotes the CR fractional sub-Laplacian operator on ℍn, Q = 2n + 2 is the homogeneous dimension of ℍn, and $\gamma \in \bigcup\nolimits_{k = 1}^n [k,((kQ)/Q-1)))$. Our argument is variational, based on a Ding-type conformal pulling-back transformation of the original problem into a problem on the CR sphere S2n + 1 combined with a suitable Hebey-Vaugon-type compactness result and group-theoretical constructions for special subgroups of the unitary group U(n + 1).

Nondegeneracy of Nodal Solutions to the Critical Yamabe Problem

2015 ◽  
Vol 340 (3) ◽  
pp. 1049-1107 ◽  
Author(s):  
Monica Musso ◽  
Juncheng Wei
Keyword(s):  
Yamabe Problem ◽  
Nodal Solutions

scholarly journals Supercritical elliptic problems on the round sphere and nodal solutions to the Yamabe problem in projective spaces

2020 ◽  
Vol 40 (4) ◽  
pp. 2495-2514
Author(s):  
Juan Carlos Fernández ◽  
◽  
Oscar Palmas ◽  
Jimmy Petean ◽  
Keyword(s):  
Elliptic Problems ◽  
Projective Spaces ◽  
Yamabe Problem ◽  
Round Sphere ◽  
Nodal Solutions

Finite Element Analysis of a Polymer- Polymer Sliding Contact for Schallamach Wave and Wear

2007 ◽  
Vol 348-349 ◽  
pp. 633-636 ◽  
Author(s):  
Muhammad Azeem Ashraf ◽  
Bijan Sobhi-Najafabadi ◽  
Özdemir Göl ◽  
D. Sugumar
Keyword(s):  
Finite Element ◽  
Polymer Surface ◽  
Sliding Contact ◽  
Quasi Steady State ◽  
Nodal Solutions ◽  
Element Analysis ◽  
Steady State Analysis ◽  
Initiation And Propagation ◽  
Wear Law ◽  
Nodal Level

Sliding polymer-polymer surface contacts, due to their inherent elastic properties, exhibit detachment waves also termed as Schallamach waves. Such waves effect the initiation and propagation of wear along the sliding contacts. This paper presents quasi steady-state analysis of such a sliding contact using finite element. The contact is modeled and nodal solutions for pressure are obtained for small sliding steps. Analysis of orthogonal pressure components at the contact nodes reveals the formation of Schallamach wave phenomenon. Further, appropriate wear law is used for calculation of wear at nodal level.

scholarly journals Existence and symmetry of least energy nodal solutions for Hamiltonian elliptic systems

2015 ◽  
Vol 104 (6) ◽  
pp. 1075-1107 ◽  
Author(s):  
Denis Bonheure ◽  
Ederson Moreira dos Santos ◽  
Miguel Ramos ◽  
Hugo Tavares
Keyword(s):  
Elliptic Systems ◽  
Nodal Solutions ◽  
Least Energy

Linear perturbations of the fractional Yamabe problem on the minimal conformal infinity

2021 ◽  
Vol 29 (2) ◽  
pp. 363-407
Author(s):  
Shengbing Deng ◽  
Seunghyeok Kim ◽  
Angela Pistoia
Keyword(s):  
Yamabe Problem ◽  
Linear Perturbations
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