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Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations -
D Wang (2019)
1Bound. Value Probl., 75
- Publisher
- Springer Journals
- Copyright
- Copyright © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2021
- ISSN
- 0126-6705
- eISSN
- 2180-4206
- DOI
- 10.1007/s40840-020-01061-z
- Publisher site
- See Article on Publisher Site
Abstract
In this article, we study the following Kirchhoff–Schrödinger–Poisson system with pure power nonlinearity -(a+b∫R3|∇u|2dx)Δu+V(x)u+K(x)ϕu=h(x)|u|p-1u,x∈R3,-Δϕ=K(x)u2,x∈R3,\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\begin{aligned} \left\{ \begin{array}{ll} -\Bigl (a+b \displaystyle \int _{\mathbb {R}^3}|\nabla u|^2{\text {d}}x\Bigr )\Delta u+V(x) u+K(x) \phi u= h(x)|u|^{p-1}u, &{}x\in \mathbb {R}^3, \\ -\Delta \phi =K(x)u^2, &{}x\in \mathbb {R}^3, \end{array} \right. \end{aligned}$$\end{document}where a, b are positive constants, and 3<p<5\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$3<p<5$$\end{document}. Under some proper assumptions on the potentials V, K and h, not requiring nonnegative property, we find a ground state solution for the above problem with the help of Nehari manifold.
Journal
Bulletin of the Malaysian Mathematical Sciences Society – Springer Journals
Published: Jan 6, 2021