Finite Morse index solutions of exponential problems

DOI10.1016/j.anihpc.2006.12.001zbMath1136.35030OpenAlexW2122285324MaRDI QIDQ2475791

E. Norman Dancer

Publication date: 11 March 2008

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/78779

zbMATH Keywords

finite Morse index solutionsexponential problemsinfinitely many bifurcations

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Nonlinear elliptic equations (35J60) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05)

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Cites Work

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• Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations
• Infinitely many turning points for some supercritical problems
• Real analyticity and non-degeneracy
• The sub-harmonic bifurcation of Stokes waves
• New Liouville theorems for linear second order degenerate elliptic equations in divergence form.
• Stable solutions on \(\mathbb R^n\) and the primary branch of some non-self-adjoint convex problems.
• Quasilinear Dirichlet problems driven by positive sources
• Finite Morse index solutions of supercritical problems
• Generic properties of nonlinear boundary value problems
• Solutions of superlinear elliptic equations and their morse indices
• Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
• Stable and finite Morse index solutions on 𝐑ⁿ or on bounded domains with small diffusion

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