Concentrating solutions for the Hénon equation in \(\mathbb R^{2}\)

DOI10.1007/BF02916763zbMath1173.35504MaRDI QIDQ1034857

Angela Pistoia, Pierpaolo Esposito, Wei, Juncheng

Publication date: 8 November 2009

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Singular perturbations in context of PDEs (35B25) Degenerate elliptic equations (35J70) Subelliptic equations (35H20)

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Cites Work

• Unnamed Item
• Unnamed Item
• Multi-peak solutions for the Hénon equation with slightly subcritical growth
• Classification of solutions of some nonlinear elliptic equations
• Construction of singular limits for a semilinear elliptic equation in dimension 2
• On the existence of blowing-up solutions for a mean field equation
• The asymptotic behaviour of the ground state solutions for Hénon equation.
• Singular limits in Liouville-type equations
• Multiple boundary concentrating solutions to Dirichlet problem of Hénon equation
• Concentrating solutions for a planar elliptic problem involving nonlinearities with large exponent
• On the Hénon equation: asymptotic profile of ground states. II
• On a class of elliptic problems in R²: symmetry and uniqueness results
• NON-RADIAL GROUND STATES FOR THE HÉNON EQUATION
• On the existence and profile of nodal solutions for a two-dimensional elliptic problem with large exponent in nonlinearity
• 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
• Blowup Solutions for a Liouville Equation with Singular Data
• ALGORITHMS AND VISUALIZATION FOR SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS
• The existence of non-topological multivortex solutions in the relativistic self-dual Chern-Simons theory
• Convergence for a Liouville equation

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