\(L^{\infty}\)-norm and energy quantization for the planar Lane-Emden problem with large exponent

DOI10.1007/s00013-018-1191-zzbMath1417.35042OpenAlexW2800740283MaRDI QIDQ667721

Filomena Pacella, Massimo Grossi, Francesca De Marchis, Isabella Ianni

Publication date: 1 March 2019

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-018-1191-z

zbMATH Keywords

positive solutionsquantizationLane-Emden problem

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (8)

Uniform a priori estimates for positive solutions of the Lane-Emden system in the plane ⋮ Asymptotic behavior of least energy nodal solutions for biharmonic Lane-Emden problems in dimension four ⋮ Sharp asymptotic behavior of radial solutions of some planar semilinear elliptic problems ⋮ Convergence for a planar elliptic problem with large exponent Neumann data ⋮ Uniform a priori estimates for positive solutions of the Lane-Emden equation in the plane ⋮ Non-degeneracy and local uniqueness of positive solutions to the Lane-Emden problem in dimension two ⋮ Morse index and uniqueness of positive solutions of the Lane-Emden problem in planar domains ⋮ Uniform bounds for solutions to elliptic problems on simply connected planar domains

Cites Work

• Morse index and sign-changing bubble towers for Lane-Emden problems
• Asymptotic analysis and sign-changing bubble towers for Lane-Emden problems
• Exact Morse index computation for nodal radial solutions of Lane-Emden problems
• Asymptotic profile of positive solutions of Lane-Emden problems in dimension two
• Symmetry and related properties via the maximum principle
• Global compactness properties of semilinear elliptic equations with critical exponential growth
• Concentrating solutions for a planar elliptic problem involving nonlinearities with large exponent
• On a Two-Dimensional Elliptic Problem with Large Exponent in Nonlinearity
• Asymptotic estimates for a two-dimensional problem with polynomial nonlinearity
• Asymptotic Estimates and Qualitative Properties of an Elliptic Problem in Dimension Two
• Single-point condensation and least-energy solutions

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