On an eigenvalue problem related to the critical exponent

DOI10.1007/s00209-004-0755-8zbMath1122.35087OpenAlexW2051887416MaRDI QIDQ1775194

Filomena Pacella, Massimo Grossi

Publication date: 4 May 2005

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-004-0755-8

zbMATH Keywords

eigenfunctionsLaplacianestimates of eigenvalues

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Estimates of eigenvalues in context of PDEs (35P15) Critical exponents in context of PDEs (35B33) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10)

Related Items (8)

Qualitative properties of multi-bubble solutions for nonlinear elliptic equations involving critical exponents ⋮ Morse Indices of Multiple Blow-Up Solutions to the Two-Dimensional Gel'fand Problem ⋮ Qualitative analysis to an eigenvalue problem of the Hénon equation ⋮ Classification of finite energy solutions to the fractional Lane-Emden-Fowler equations with slightly subcritical exponents ⋮ Spectral estimates of least energy solutions to the Brezis-Nirenberg problem with a variable coefficient ⋮ Supercritical elliptic problem with nonautonomous nonlinearities ⋮ On the spectrum of a nonlinear planar problem ⋮ Morse index and uniqueness of positive solutions of the Lane-Emden problem in planar domains

Cites Work

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• Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent
• Proof of two conjectures of H. Brezis and L. A. Peletier
• Symmetry and related properties via the maximum principle
• A note on the Sobolev inequality
• On the nodal line of the second eigenfunction of the Laplacian in \(\mathbb{R}^ 2\)
• On a variational problem with lack of compactness: The topological effect of the critical points at infinity
• ON THE SHAPE OF THE SOLUTIONS OF SOME SEMILINEAR ELLIPTIC PROBLEMS
• Inequalities for the Green Function and Boundary Continuity of the Gradient of Solutions of Elliptic Differential Equations.
• A uniqueness result for a semilinear elliptic equation in symmetric domains

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