Ground state solutions of Nehari-Pohozaev type for Schrödinger-Poisson problems with general potentials
By Xianhua Tang, Sitong Chen. 2017
141 citations recorded by the source corpus.
This paper is dedicated to studying the following Schrodinger-Poisson problem \begin{document} $\left\{ \begin{array}{ll} -\triangle u+V(x)u+φ u=f(u), \ \ \ \ x∈ \mathbb{R}^{3},\\ -\triangle φ=u^2, \ \ \ \ x∈ \mathbb{R}^{3}, \end{array} \right. $ \end{document} where \begin{document}$V(x)$\end{document} is weakly differentiable and \begin{document}$f∈ \mathcal{C}(\mathbb{R}, \mathbb{R})$\end{document} . By introducing some new tricks, we prove the above problem admits a ground state solution of Nehari-Pohozaev type and a least energy solution under mild assumptions on \begin{document}$V$\end{document} and \begin{document}$f$\end{document} . Our results generalize and improve the ones in [D. Ruiz, J. Funct. Anal. 237 (2006) 655-674], [J.J. Sun, S.W. Ma, J. Differential Equations 260 (2016) 2119-2149] and some related literature.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/8a609ba48f6e9f18e4de3d817535ba54e943574c
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In Applied Mathematics
- Sitong Chen
- Xianhua Tang
- Binlin Zhang
- Vicentiu D. Rădulescu
- Mingqi Xiang
- A. Fiscella
- Patrizia Pucci
- Patrick Winkert
In Computational Theory and Mathematics
Citations in the corpus
- Ground state solutions of Nehari–Pohozaev type for Kirchhoff-type problems with general potentials (2017, methodology): “We gave a simpler and more direct proof in [33].”
- Existence and non-existence results for Kirchhoff-type problems with convolution nonlinearity (2018, methodology): “Althoughwemainly follow the procedure of [36], we have to facemany new difficulties due to themutual competing effect between (∫R3 |∇u| 2 dx)∆u and (Iα ∗ F(u))f(u).”