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

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).

scholarly journals Nodal solutions to critical growth elliptic problems under Steklov boundary conditions

2009 ◽  
Vol 8 (2) ◽  
pp. 533-557 ◽  
Author(s):  
Elvise Berchio ◽  
◽  
Filippo Gazzola ◽  
Dario Pierotti ◽  
◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Elliptic Problems ◽  
Critical Growth ◽  
Nodal Solutions

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
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