INFINITELY MANY SOLUTIONS FOR A ZERO MASS SCHRÖDINGER-POISSON-SLATER PROBLEM WITH CRITICAL GROWTH | Zendy

Liu Yang | Zendy; Zhisu Liu | Zendy

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INFINITELY MANY SOLUTIONS FOR A ZERO MASS SCHRÖDINGER-POISSON-SLATER PROBLEM WITH CRITICAL GROWTH

Author(s) -

Liu Yang,

Zhisu Liu

Publication year - 2019

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/20180273

Subject(s) - truncation (statistics) , mathematics , poisson distribution , combinatorics , compact space , mathematical physics , zero (linguistics) , star (game theory) , mathematical analysis , physics , statistics , philosophy , linguistics

In this paper, we are concerned with the following SchrödingerPoisson-Slater problem with critical growth: −∆u+ (u ? 1 |4πx| )u = μk(x)|u| u+ |u|u in R. We use a measure representation concentration-compactness principle of Lions to prove that the (PS)c condition holds locally. Via a truncation technique and Krasnoselskii genus theory, we further obtain infinitely many solutions for μ ∈ (0, μ∗) with some μ∗ > 0.

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