ASYMPTOTICS AND SYMMETRIES OF LEAST ENERGY NODAL SOLUTIONS OF LANE–EMDEN PROBLEMS WITH SLOW GROWTH

DOI10.1142/S0219199708002910zbMath1156.35037MaRDI QIDQ3526532

Denis Bonheure, Jean Van Schaftingen, Christopher Grumiau, Vincent Bouchez

Publication date: 25 September 2008

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

zbMATH Keywords

symmetryvariational methodssemilinear elliptic problemsymmetry breakingNehari manifoldsuperlinear elliptic boundary value problemnodal Nehari setleast energy nodal solution

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear elliptic equations (35J60) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Geometric theory, characteristics, transformations in context of PDEs (35A30) Variational methods for second-order elliptic equations (35J20)

Related Items (12)

On the least-energy solutions of the pure Neumann Lane-Emden equation ⋮ Multiple radial positive solutions of semilinear elliptic problems with Neumann boundary conditions ⋮ Nonlinear Schrödinger problems: symmetries of some variational solutions ⋮ A Morse index formula for radial solutions of Lane-Emden problems ⋮ Asymptotic symmetries for fractional operators ⋮ Lane-Emden problems: asymptotic behavior of low energy nodal solutions ⋮ Properties of ground states of nonlinear Schrödinger equations under a weak constant magnetic field ⋮ A computer assisted proof of the symmetries of least energy nodal solutions on squares ⋮ Morse index computation for radial solutions of the Hénon problem in the disk ⋮ Nodal line structure of least energy nodal solutions for Lane-Emden problems ⋮ On a property of the nodal set of least energy sign-changing solutions for quasilinear elliptic equations ⋮ The asymptotically linear Hénon problem

Cites Work

• Partial symmetry of least energy nodal solutions to some variational problems
• Symmetry and related properties via the maximum principle
• A sign-changing solution for a superlinear Dirichlet problem
• Qualitative properties of nodal solutions of semilinear elliptic equations in radially symmetric domains
• Dual variational methods in critical point theory and applications
• NON-RADIAL GROUND STATES FOR THE HÉNON EQUATION
• A mountain pass method for the numerical solution of semilinear elliptic problems
• A numerical investigation of sign-changing solutions to superlinear elliptic equations on symmetric domains

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