Elliptic Problems Involving Mixed Local-Nonlocal Operator in the Hyperbolic Space

2025/05/19 by Gupta, Diksha, Sreenadh, Konijeti
#35B09 #35B38 #35J20 #35J61 #35R01 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.12936

Abstract

This paper explores the existence of solutions to a class of nonlinear elliptic equations involving a mixed local-nonlocal operator of the form -Δ_\mathbbB^N + (-Δ_\mathbbB^N)^s, with 0 < s < 1, set in the hyperbolic space \mathbbB^N. By employing variational methods, we address both subcritical and critical nonlinearities, establishing the existence of weak solutions under appropriate conditions.

Citations

• Poincaré-Sobolev equations with the critical exponent and a potential in the hyperbolic space
• Existence, symmetry and regularity of ground states of a non linear choquard equation in the hyperbolic space
• Fractional Sobolev spaces on Riemannian manifolds
• On a class of elliptic equations with Critical Perturbations in the hyperbolic space
• The fractional p-Laplacian on hyperbolic spaces
• Multiplicity of positive solutions for a class of nonhomogeneous elliptic equations in the hyperbolic space
• A Brezis-Nirenberg type result for mixed local and nonlocal operators
• Existence of high energy positive solutions for a class of elliptic equations in the hyperbolic space
• Harnack inequality for fractional Laplacian-type operators on hyperbolic spaces
• Mixed local and nonlocal Sobolev inequalities with extremal and associated quasilinear singular elliptic problems
• Semilinear elliptic equations involving mixed local and nonlocal operators
• Mixed local and nonlocal elliptic operators: regularity and maximum\n principles
• Green's functions of Paneitz and GJMS operators on hyperbolic spaces and sharp Hardy-Sobolev-Maz'ya inequalities on half spaces
• Nonlocal elliptic equations in bounded domains: a survey
• The Brezis-Nirenberg result for the fractional Laplacian
• Large solutions to elliptic equations involving fractional Laplacian
• Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties
• Some constructions for the fractional Laplacian on noncompact manifolds
• Stability and qualitative properties of radial solutions of the Lane-Emden-Fowler equation on Riemannian models
• Sign changing solutions of the Brezis-Nirenberg problem in the\n Hyperbolic space
• Hitchhiker's guide to the fractional Sobolev spaces
• Hitchhikerʼs guide to the fractional Sobolev spaces
• Classification of radial solutions to the Emden-Fowler equation on the hyperbolic space
• Fractional Laplacian in Conformal Geometry

Related

• Mixed local and nonlocal semilinear elliptic equation with strongly singular and critical Choquard nonlinearity
• Multiplicity of solutions for mixed local-nonlocal elliptic equations with singular nonlinearity
• Combined effects in mixed local-nonlocal stationary problems
• On a class of elliptic equations with Critical Perturbations in the hyperbolic space
• Existence of solutions for nonlinear equations with mixed local and nonlocal operators