Decay in Energy Space for the Solutions of Generalized Schrödinger-Hartree Equation Perturbed by a Potential

Authors

  • Elena Nikolova Department of Mathematical Analysis and Differential Equations, Technical University of Sofia
  • Mirko Tarulli Technical University of Sofia and Bulgarian Academy of Sciences and Università di Pisa
  • George Venkov Department of Mathematical Analysis and Differential Equations, Technical University of Sofia

DOI:

https://doi.org/10.7546/CRABS.2022.11.02

Keywords:

nonlinear Schr¨odinger equations, Schr¨odinger operators, scattering theory

Abstract

We prove, in any space dimension d≥3, the decay in the energy space for the defocusing Schrödinger–Hartree (SCH) equations with mass-energy intercritical non-local nonlinearities and perturbed by a potential. We will show also new Morawetz inequalities and estimates, generalizing the previous results appearing in [1].

Author Biographies

Elena Nikolova, Department of Mathematical Analysis and Differential Equations, Technical University of Sofia

Mailing Address:
Department of Mathematical Analysis and Differential Equations,
Technical University of Sofia
8 Kliment Ohridski Blvd
1000 Sofia, Bulgaria

E-mail: elenikolova@tu-sofia.bg

Mirko Tarulli, Technical University of Sofia and Bulgarian Academy of Sciences and Università di Pisa

Mailing Address:
Department of Mathematical Analysis and Differential Equations,
Technical University of Sofia
8 Kliment Ohridski Blvd
1000 Sofia, Bulgaria

and

Institute of Mathematics and Informatics,
Bulgarian Academy of Sciences
Akad. G. Bonchev St, Bl. 8
1113 Sofia, Bulgaria

and

Dipartimento di Matematica
Università di Pisa
Largo Bruno Pontecorvo 5
56100 Pisa, Italy

E-mail: mta@tu-sofia.bg

George Venkov, Department of Mathematical Analysis and Differential Equations, Technical University of Sofia

Mailing Address:
Department of Mathematical Analysis and Differential Equations,
Technical University of Sofia
8 Kliment Ohridski Blvd
1000 Sofia, Bulgaria

E-mail: gvenkov@tu-sofia.bg

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Published

30-11-2022

How to Cite

[1]
E. Nikolova, M. Tarulli, and G. Venkov, “Decay in Energy Space for the Solutions of Generalized Schrödinger-Hartree Equation Perturbed by a Potential”, C. R. Acad. Bulg. Sci. , vol. 75, no. 11, pp. 1559–1572, Nov. 2022.

Issue

Section

Mathematics