Spectral theory for linearized \(p\)-Laplace equations

DOI10.1016/j.na.2011.03.009zbMath1217.35124OpenAlexW1992627595MaRDI QIDQ540247

Berardino Sciunzi, Daniele Castorina, Pierpaolo Esposito

Publication date: 1 June 2011

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.2011.03.009

zbMATH Keywords

Harnack inequalityMorse indexspectral theory\(p\)-Laplace equationregularity of eigenfunctions

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) General topics in linear spectral theory for PDEs (35P05) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Positive solutions to PDEs (35B09) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (6)

Quasilinear elliptic equations with singular nonlinearity ⋮ Hopf lemma and regularity results for quasilinear anisotropic elliptic equations ⋮ Weighted Sobolev spaces and Morse estimates for quasilinear elliptic equations ⋮ Second-order derivative of domain-dependent functionals along Nehari manifold trajectories ⋮ Regularity of the extremal solution for singular \(p\)-Laplace equations ⋮ On qualitative properties of solutions for elliptic problems with thep-Laplacian through domain perturbations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Regularity, monotonicity and symmetry of positive solutions of \(m\)-Laplace equations
• Harnack inequalities, maximum and comparison principles, and regularity of positive solutions of \(m\)-Laplace equations
• On the classification of solutions of the Lane-Emden equation on unbounded domains of \(\mathbb R^N\)
• Degenerate elliptic equations with singular nonlinearities
• Multiple positive solutions for a critical quasilinear equation via Morse theory
• \(p\)-MEMS equation on a ball
• Linking solutions for \(p\)-Laplace equations with nonlinearity at critical growth
• Regularity for a more general class of quasilinear equations
• Elliptic partial differential equations of second order
• Liouville results for \(m\)-Laplace equations of Lane-Emden-Fowler type
• Semi-stable and extremal solutions of reaction equations involving the \(p\)-Laplacian
• Linking over cones and nontrivial solutions for \(p\)-Laplace equations with \(p\)-superlinear nonlinearity
• On the Equation div( | ∇u | p-2 ∇u) + λ | u | p-2 u = 0
• C1 + α local regularity of weak solutions of degenerate elliptic equations
• Symmetry of solutions to semilinear elliptic equations via Morse index
• COMPACTNESS OF A NONLINEAR EIGENVALUE PROBLEM WITH A SINGULAR NONLINEARITY
• On the classification of solutions of -Δ𝑢=𝑒^{𝑢} on ℝ^{ℕ}: Stability outside a compact set and applications
• Boundary regularity for solutions of degenerate elliptic equations
• On Harnack's theorem for elliptic differential equations
• Compactness along the branch of semistable and unstable solutions for an elliptic problem with a singular nonlinearity

This page was built for publication: Spectral theory for linearized \(p\)-Laplace equations