On the Schrodinger equation in R^N under the effect of a general nonlinear term

2008/02/13 by Antonio Azzollini, Alessio Pomponio, Azzollini, Antonio +1
Computer Science · Mathematics · #35J60 #58E05 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.AP #msc:35J60 #msc:58E05

paper · pdf · doi:10.48550/arxiv.0802.1844

18 pages

arxiv created 2008/02/13 · openalex publication_date 2008/02/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove the existence of a positive solution to the equation -Δu + V(x)u=g(u) in R^N, assuming the general hypotheses on the nonlinearity introduced by Berestycki & Lions. Moreover we show that a minimizing problem, related to the existence of a ground state, has no solution.

Citations

• Existence of solitary waves in higher dimensions

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