New Results for Finite Morse Index Solutions on ℝN and applications

DOI10.1515/ans-2010-0304zbMath1216.35050OpenAlexW2510083731MaRDI QIDQ2998670

E. Norman Dancer

Publication date: 18 May 2011

Published in: Advanced Nonlinear Studies (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ans-2010-0304

zbMATH Keywords

Morse indexbounded domainhalf spacelinearized stable solutions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Stability in context of PDEs (35B35) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61) Variational problems in abstract bifurcation theory in infinite-dimensional spaces (58E07)

Related Items (3)

On the number of stable positive solutions of weakly nonlinear elliptic equations when the diffusion is small ⋮ Monotonicity and nonexistence results to cooperative systems in the half space ⋮ Recent progress on stable and finite Morse index solutions of semilinear elliptic equations

Cites Work

• Some remarks on half space problems
• On the classification of solutions of the Lane-Emden equation on unbounded domains of \(\mathbb R^N\)
• On the influence of domain shape on the existence of large solutions of some superlinear problems
• Symmetry and related properties via the maximum principle
• On positive solutions of -Delta(u)=F(x,u)
• Introduction à la théorie des points critiques et applications aux problèmes elliptiques
• Finite Morse index solutions of supercritical problems
• On the Number of Positive Solutions of Weakly Non-Linear Elliptic Equations when a Parameter is Large
• Stable and finite Morse index solutions on 𝐑ⁿ or on bounded domains with small diffusion

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