Existence and behavior of positive solutions for a class of linearly coupled systems with discontinuous nonlinearities in $${\mathbb {R}}^N$$

Albuquerque, José Carlos de; Santos, Gelson G. dos; Figueiredo, Giovany M.

doi:10.1007/s11784-021-00858-0

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2022

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“…In the celebrated paper [13], del Pino and Felmer [13] discovered that the solution of equation (1.3) is concentrated at the local minimum points of V by constructing a penalization function under (V 1 ), (V 2 ) and g being subcritical growth. After their eorts, the existence, multiplicity and concentration of solutions for equation (1.3) have attracted attention of many mathematics researchers, we cite [25,12,21,30].…”

Section: Introductionmentioning

confidence: 99%

Multiplicity and concentration of positive solutions for quasilinear Schrödinger-Poisson system with critical nonlinearity

Zhang

wen

Zhao

2022

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In this paper, we are interested in the following Schrödinger-Poisson system { − ε p ∆ p u + V ( x ) | u | p − 2 u + ϕ | u | p − 2 u = f ( u )+ | u | p ∗ − 2 u in R 3 , − ε 2 ∆ ϕ = | u | p in R 3 , where ε>0 is a parameter, 3 2 < p < 3 , ∆ p u = div ( | ∇ u | p − 2 ∇ u ) , p ∗ = 3 p 3 − p , V : R 3 → R is a positive function with a local minimum and f is subcritical growth. Based on the penalization method, Nehari manifold techniques and Ljusternik-Schnirelmann category theory, we obtain the multiplicity and concentration of positive solutions.

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Section: Introductionmentioning

confidence: 99%