Existence of nodal solutions of semilinear equations in \({\mathbb{R}}^ n\)

DOI10.1016/0022-0396(90)90121-5zbMath0706.35046OpenAlexW1975989209MaRDI QIDQ919181

Manoussos G. Grillakis

Publication date: 1990

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(90)90121-5

zbMATH Keywords

radial solutionnodal solutionssemilinearprescribed number of zeros

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Degree, winding number (55M25)

Related Items (14)

A nodal solution of the scalar field equation at the second minimax level ⋮ Existence of nodal fast-decay solutions to Δu+K(|x|)|u|p−1u = 0 IN Rn ⋮ The focusing logarithmic Schrödinger equation: analysis of breathers and nonlinear superposition ⋮ Infinitely many radial solutions to a boundary value problem in a ball ⋮ INFINITELY MANY NODAL SOLUTIONS FOR A WEAKLY COUPLED NONLINEAR SCHRÖDINGER SYSTEM ⋮ On the second minimax level of the scalar field equation and symmetry breaking ⋮ Asymptotic stability of solitons of the gKdV equations with general nonlinearity ⋮ Norm Estimates for Radially Symmetric Solutions of Semilinear Elliptic Equations ⋮ High-speed excited multi-solitons in nonlinear Schrödinger equations ⋮ New singular solutions of the nonlinear Schrödinger equation ⋮ Singular ring solutions of critical and supercritical nonlinear Schrödinger equations ⋮ The geometry of nonlinear Schrödinger standing waves: Pure power nonlinearities ⋮ Nodal solutions for a sublinear elliptic equation ⋮ The ground state of a Gross-Pitaevskii energy with general potential in the Thomas-Fermi limit

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• On the Infinitely Many Solutions of a Semilinear Elliptic Equation
• Explicit construction of all spherically symmetric solitary waves for a nonlinear wave equation in multiple dimensions
• Uniqueness of solutions of semilinear Poisson equations

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