Supercritical finite Morse index solutions

DOI10.1016/J.NA.2005.11.012zbMath1387.58015OpenAlexW2069879530MaRDI QIDQ860738

E. Norman Dancer

Publication date: 9 January 2007

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2005.11.012

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05)

Related Items (2)

Partial regularity of stable solutions to the supercritical equations and its applications ⋮ Recent progress on stable and finite Morse index solutions of semilinear elliptic equations

Cites Work

• Superlinear problems on domains with holes of asymptotic shape and exterior problems
• Infinitely many turning points for some supercritical problems
• New Liouville theorems for linear second order degenerate elliptic equations in divergence form.
• Symmetry of positive solutions of \(\Delta u + u^ p = 0\) in \(\mathbf R^ n\)
• Stable solutions on \(\mathbb R^n\) and the primary branch of some non-self-adjoint convex problems.
• Liouville-type results for solutions of \(-\Delta u=|u|^{p-1}u\) on unbounded domains of \(\mathbb R^N\)
• 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 R^n or on bounded domains with small diffusion II

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