MULTIPLICITY RESULTS FOR A QUASILINEAR ELLIPTIC SYSTEM VIA MORSE THEORY

DOI10.1142/S0219199705001714zbMath1079.58008MaRDI QIDQ3023929

Silvia Cingolani, Giuseppina Vannella, Monica Lazzo

Publication date: 6 July 2005

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

zbMATH Keywords

critical groupsMorse theoryquasilinear elliptic systemsdegenerate critical points

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational methods for elliptic systems (35J50) Perturbations in context of PDEs (35B20)

Related Items (12)

A multiplicity result via Ljusternick-Schnirelmann category and Morse theory for a fractional Schrödinger equation in \(\mathbb{R}^N\) ⋮ Multiple solutions for a Schrödinger–Bopp–Podolsky system with positive potentials ⋮ Weighted Sobolev spaces and Morse estimates for quasilinear elliptic equations ⋮ The Brezis-Nirenberg type problem for the \(p\)-Laplacian \((1 < p < 2)\): multiple positive solutions ⋮ Marino-Prodi perturbation type results and Morse indices of minimax critical points for a class of functionals in Banach spaces ⋮ Regularity and Morse Index of the Solutions to Critical Quasilinear Elliptic Systems ⋮ Multiplicity results for the fractional Laplacian in expanding domains ⋮ Towards a Morse theory on Banach spaces via ultrafunctions ⋮ Multiple positive solutions for a critical quasilinear equation via Morse theory ⋮ On the multiplicity of positive solutions for \(p\)-Laplace equations via Morse theory ⋮ Multiplicity and nondegeneracy of positive solutions to quasilinear equations on compact Riemannian manifolds ⋮ Multiple positive solutions for a p-Laplace Benci–Cerami type problem (1 < p < 2), via Morse theory

Cites Work

• An eigenvalue problem for a quasilinear elliptic field equation
• The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems
• A new approach to the Morse-Conley theory and some applications
• Multiple positive solutions of some elliptic problems via the Morse theory and the domain topology
• Solitons in several space dimensions: Derrick's problem and infinitely many solutions
• Critical groups computations on a class of Sobolev Banach spaces via Morse index
• On differentiable functions with isolated critical points
• Morse Theory. (AM-51)
• Soliton Like Solutions of a Lorentz Invariant Equation in Dimension 3
• An Infinite Dimensional Version of Sard's Theorem

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