Nodal solutions for elliptic equation involving the GJMS operators on compact manifolds

Bekiri, Mohamed; Benalili, Mohammed

doi:10.1080/17476933.2019.1579209

Complex Variables and Elliptic Equations

2019

DOI: 10.1080/17476933.2019.1579209

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Nodal solutions for elliptic equation involving the GJMS operators on compact manifolds

Mohamed Bekiri

Mohammed Benalili

Abstract: In this paper we investigate the existence of nodal solutions to elliptic problem involving the GJMS operators on Riemannian manifold with boundary.

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2024

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Equivariant Solutions to the Optimal Partition Problem for the Prescribed Q-Curvature Equation

Fernández,

Palmas,

Torres Orozco

2024

J Geom Anal

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We study the optimal partition problem for the prescribed constant Q-curvature equation induced by the higher-order conformal operators under the effect of cohomogeneity one actions on Einstein manifolds with positive scalar curvature. This allows us to give a precise description of the solution domains and their boundaries in terms of the orbits of the action. We also prove the existence of least energy symmetric solutions to a weakly coupled elliptic system of prescribed Q-curvature equations under weaker assumptions and conclude a multiplicity result of sign-changing solutions to the prescribed constant Q-curvature problem induced by the Paneitz-Branson operator. Moreover, we study the coercivity of GJMS operators on Ricci solitons, compute the Q-curvature of these manifolds, and give a multiplicity result for the sign-changing solutions to the Yamabe problem with a prescribed number of nodal domains on the Koiso–Cao Ricci soliton.

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Equivariant Solutions to the Optimal Partition Problem for the Prescribed Q-Curvature Equation

Fernández,

Palmas,

Torres Orozco

2024

J Geom Anal

View full text Add to dashboard Cite

show abstract

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Nodal solutions for elliptic equation involving the GJMS operators on compact manifolds

Abstract: In this paper we investigate the existence of nodal solutions to elliptic problem involving the GJMS operators on Riemannian manifold with boundary.

Cited by 1 publication

References 20 publications

Equivariant Solutions to the Optimal Partition Problem for the Prescribed Q-Curvature Equation

Equivariant Solutions to the Optimal Partition Problem for the Prescribed Q-Curvature Equation

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