Nondegeneracy of positive solutions of semilinear elliptic problems in the hyperbolic space

DOI10.1142/S0219199714500199zbMath1314.58013arXiv1304.3216MaRDI QIDQ5496350

Kunnath Sandeep, Debdip Ganguly

Publication date: 30 January 2015

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.3216

zbMATH Keywords

semilinear elliptic equationshyperbolic spacenondegeneracy

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61) Positive solutions to PDEs (35B09) PDEs on manifolds (35R01)

Related Items (12)

The solution gap of the Brezis-Nirenberg problem on the hyperbolic space ⋮ Existence, uniqueness, and exponential stability for the Kirchhoff equation in whole hyperbolic space ⋮ Exponential decay for semilinear wave equation with localized damping in the hyperbolic space ⋮ Existence of high energy-positive solutions for a class of elliptic equations in the hyperbolic space ⋮ On nonlinear Schrödinger equations on the hyperbolic space ⋮ On the nonlinear Schrödinger equation on the Poincaré ball model ⋮ Concentration phenomenon in the critical exponent problems on hyperbolic space ⋮ A CLASS OF CRITICAL KIRCHHOFF PROBLEM ON THE HYPERBOLIC SPACE ⋮ Partial symmetry and existence of least energy solutions to some nonlinear elliptic equations on Riemannian models ⋮ Theoretical developments in the study of partial differential equations ⋮ Kirchhoff-type problems on a geodesic ball of the hyperbolic space ⋮ Qualitative properties of stationary solutions of the NLS on the hyperbolic space without and with external potentials

Cites Work

• Uniqueness of positive solutions of semilinear elliptic equations and related eigenvalue problems
• Qualitative properties of positive solutions of semilinear elliptic equations in symmetric domains via the maximum principle
• A few symmetry results for nonlinear elliptic PDE on noncompact manifolds
• Hardy-Sobolev extremals, hyperbolic symmetry and scalar curvature equations
• Poincaré-Sobolev equations in the hyperbolic space
• On the Grushin operator and hyperbolic symmetry
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Uniqueness of positive radial solutions of semilinear elliptic equations in R^Nand séré's non—degeneracy condition

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