Ground states for the pseudo-relativistic Hartree equation with external potential

Silvia Cingolani; Simone Secchi

doi:10.1017/S0308210513000450

Abstract

We prove the existence of positive ground state solutions to the pseudo-relativistic Schrödinger equation

where N ≥ 3, m > 0, V is a bounded external scalar potential and W is a radially symmetric convolution potential satisfying suitable assumptions. We also provide some asymptotic decay estimates of the found solutions.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Xie, Tao Xiao, Lu and Wang, Jun 2015. Existence of Multiple Positive Solutions for Choquard Equation with Perturbation. Advances in Mathematical Physics, Vol. 2015, Issue. , p. 1.

Cingolani, Silvia and Secchi, Simone 2015. Semiclassical analysis for pseudo-relativistic Hartree equations. Journal of Differential Equations, Vol. 258, Issue. 12, p. 4156.

Carles, Rémi Lucha, Wolfgang and Moulay, Emmanuel 2015. Higher-order Schrödinger and Hartree–Fock equations. Journal of Mathematical Physics, Vol. 56, Issue. 12,

Chen, Yan-Hong and Liu, Chungen 2016. Ground state solutions for non-autonomous fractional Choquard equations. Nonlinearity, Vol. 29, Issue. 6, p. 1827.

Ikoma, Norihisa 2017. Existence of solutions of scalar field equations with fractional operator. Journal of Fixed Point Theory and Applications, Vol. 19, Issue. 1, p. 649.

Moroz, Vitaly and Van Schaftingen, Jean 2017. A guide to the Choquard equation. Journal of Fixed Point Theory and Applications, Vol. 19, Issue. 1, p. 773.

Secchi, Simone 2017. Concave-convex nonlinearities for some nonlinear fractional equations involving the Bessel operator. Complex Variables and Elliptic Equations, Vol. 62, Issue. 5, p. 654.

Secchi, Simone 2017. On Some Nonlinear Fractional Equations Involving the Bessel Operator. Journal of Dynamics and Differential Equations, Vol. 29, Issue. 3, p. 1173.

Secchi, Simone 2018. Existence of solutions for a semirelativistic Hartree equation with unbounded potentials. Forum Mathematicum, Vol. 30, Issue. 1, p. 129.

Cingolani, Silvia and Secchi, Simone 2018. Intertwining solutions for magnetic relativistic Hartree type equations. Nonlinearity, Vol. 31, Issue. 5, p. 2294.

Choi, Woocheol Hong, Younghun and Seok, Jinmyoung 2018. Semilinear elliptic equations with the pseudo-relativistic operator on a bounded domain. Nonlinear Analysis, Vol. 173, Issue. , p. 123.

Bueno, H. Miyagaki, O.H. and Pereira, G.A. 2019. Remarks about a generalized pseudo-relativistic Hartree equation. Journal of Differential Equations, Vol. 266, Issue. 1, p. 876.

Xia, Aliang 2019. Multiplicity and concentration results for magnetic relativistic Schrödinger equations. Advances in Nonlinear Analysis, Vol. 9, Issue. 1, p. 1161.

Shi, Xiaoyan Zhao, Yulin and Chen, Haibo 2019. Existence of Solutions for Nonhomogeneous Choquard Equations Involving p-Laplacian. Mathematics, Vol. 7, Issue. 9, p. 871.

Wang, Qingxuan and Li, Xin 2020. Asymptotic analysis of boosted ground states of boson stars. Mathematical Methods in the Applied Sciences, Vol. 43, Issue. 2, p. 704.

Belchior, P. Bueno, H. Miyagaki, O.H. and Pereira, G.A. 2020. Asymptotic behavior of ground states of generalized pseudo-relativistic Hartree equation. Asymptotic Analysis, Vol. 118, Issue. 4, p. 269.

Van Thin, Nguyen 2020. Multiplicity of solutions for fractional equation involving the Bessel operator in RN. Mathematische Nachrichten, Vol. 293, Issue. 10, p. 2011.

Chen, Caisheng 2020. Existence of Solutions for Fractional-Choquard Equation with a Critical Exponential Growth in $${\mathbb {R}}^N$$. Mediterranean Journal of Mathematics, Vol. 17, Issue. 5,

Huang, Zhihua Yang, Jianfu and Yu, Weilin 2021. Nodal solutions for pseudo-relativistic Hartree equations. Journal of Mathematical Analysis and Applications, Vol. 493, Issue. 1, p. 124474.

Choi, Woocheol and Seok, Jinmyoung 2021. Limit behaviors of solutions to the pseudo-relativistic Lane-Emden equation. Journal of Mathematical Analysis and Applications, Vol. 495, Issue. 1, p. 124726.

Download full list

Article contents

Ground states for the pseudo-relativistic Hartree equation with external potential

Abstract

Access options

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

Ground states for the pseudo-relativistic Hartree equation with external potential

Abstract

Access options

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests