Multiplicity of solutions of a zero mass nonlinear equation on a Riemannian manifold

DOI10.1016/j.jde.2008.03.002zbMath1152.58018arXiv0707.0976OpenAlexW2023531667MaRDI QIDQ952098

Daniela Visetti

Publication date: 6 November 2008

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.0976

zbMATH Keywords

multiplicityMorse theoryLjusternik-Schnirelmann categoryelliptic equations on manifolds

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Elliptic equations on manifolds, general theory (58J05)

Related Items (14)

A multiplicity result via Ljusternick-Schnirelmann category and Morse theory for a fractional Schrödinger equation in \(\mathbb{R}^N\) ⋮ On the existence of nodal solutions for a nonlinear elliptic problem on symmetric Riemannian manifolds ⋮ Multipeak solutions for asymptotically critical elliptic equations on Riemannian manifolds ⋮ Clustered solutions for supercritical elliptic equations on Riemannian manifolds ⋮ Multiple solutions for a Schrödinger–Bopp–Podolsky system with positive potentials ⋮ Existence of solutions to modified nonlinear Schrödinger equations on non-compact Riemannian manifolds ⋮ Some generic properties of non degeneracy for critical points of functionals and applications ⋮ Solutions to a singularly perturbed supercritical elliptic equation on a Riemannian manifold concentrating at a submanifold ⋮ Generic properties of critical points of the scalar curvature for a Riemannian manifold ⋮ Multiplicity results for the fractional Laplacian in expanding domains ⋮ The role of the scalar curvature in a nonlinear elliptic problem on Riemannian manifolds ⋮ Existence of solution for a class of quasilinear Schrödinger equation in \(\mathbb{R}^N\) with zero-mass ⋮ Positive solutions for a singularly perturbed nonlinear elliptic problem on manifolds via Morse theory ⋮ Multiplicity and nondegeneracy of positive solutions to quasilinear equations on compact Riemannian manifolds

Cites Work

• Unnamed Item
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• Nonlinear scalar field equations. I: Existence of a ground state
• The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems
• Lectures on the Ekeland variational principle with applications and detours. Lectures delivered at the Indian Institute of Science, Bangalore, India under the T.I.F.R.-I.I.Sc. programme in applications of mathematics
• Existence of solitary waves in higher dimensions
• Multiple positive solutions of some elliptic problems via the Morse theory and the domain topology
• On the multiplicity of solutions of a nonlinear elliptic problem on Riemannian manifolds
• A Note on an Equation with Critical Exponent
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
• Morse Theory. (AM-51)
• Solutions in Exterior Domains of Null Mass Nonlinear Field Equations

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