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- W3098829608 abstract "In this paper, we study the following Schr{o}dinger-Born-infeld system with a general nonlinearity $$ left{ begin{array}{ll} -triangle u+u+phi u=f(u)+mu|u|^4u,,&mbox{in},,R^3, -textrm{div}displaystylebigg(frac{nablaphi}{sqrt{1-|nablaphi|^2}}bigg)=u^2&mbox{in},,R^3, u(x)rightarrow0,,,phi(x)rightarrow0,&,text{as},,xrightarrowinfty, end{array} right. $$ where $mugeq0$ and $fin C(R,R)$ satisfies suitable assumptions. This system arises from a suitable coupling of the nonlinear Schr{o}dinger 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 $f(u)=|u|^{p-1}u$ for $pin(2,{5}/{2}]$ and $mu=0$ which was left in cite{Azzollini19} as an open problem." @default.
- W3098829608 created "2020-11-23" @default.
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- W3098829608 date "2020-11-19" @default.
- W3098829608 modified "2023-09-25" @default.
- W3098829608 title "A perturbation approach for the Schrodinger-Born-Infeld system: solutions in the subcritical and critical case" @default.
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- W3098829608 doi "https://doi.org/10.48550/arxiv.2011.09793" @default.
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