Multiplicity of positive solutions for nonlinear field equations in \R^N

2009/01/28 by Claudio Bonanno, Bonanno, Claudio
Engineering · Mathematics · #35L60 #35Q51 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.0901.4459

openalex publication_date 2009/01/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper we study the multiplicity of positive solutions for nonlinear elliptic equations on \R^N. The number of solutions is greater or equal than the number of disjoint intervals on which the nonlinear term is negative. Applications are given to multiplicity of standing waves for the nonlinear Schrödinger and Klein-Gordon equations.

Citations

• Solitons for the nonlinear Klein-Gordon equation
• Nonlinear scalar field equations, I existence of a ground state

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