A perturbation approach for the Schrodinger-Born-Infeld system: Solutions in the subcritical and critical case

[摘要] In this paper, we study the following Schrodinger-Born-Infeld system with a general nonlinearity {-Delta u + u + phi u = integral(u) + mu vertical bar mu vertical bar(4)u in R-3, -div(del phi/root 1 - vertical bar del phi vertical bar(2)) = u(2) in R-3, u(x) -> 0, phi(x) -> 0, as x -> infinity, where mu >= 0 and f is an element of C(R,R) satisfies suitable assumptions. This system arises from a suitable coupling of the nonlinear Schrodinger equation and the Born-Infeld theory. We use a new perturbation approach to prove the existence and multiplicity of nontrivial solutions of the above system in the subcritical and critical case. We emphasise that our results cover the case f (u) = vertical bar u vertical bar(p-1)u for p is an element of (2, 5/2] and mu = 0 which was left in [2] as an open problem. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-11-15

[关键词] Schrodinger-Born-Infeld system;Subcritical and critical growth;Variational methods;Perturbation approach