Cite

1. K. Ruedenberg and C. W. Scherr, Free-electron network model for conjugated systems. I. Theory, The Journal of Chemical Physics, vol. 21, no. 9, pp. 1565–1581, 1953.Search in Google Scholar

2. F. A. Mehmeti, Nonlinear Waves in Networks. Mathematical Research Series, Akademie Verlag, 1994.Search in Google Scholar

3. R. Adami, C. Cacciapuoti, D. Finco, and D. Noja, Fast solitons on star graphs, Reviews in Mathematical Physics, vol. 23, no. 04, pp. 409–451, 2011.10.1142/S0129055X11004345Search in Google Scholar

4. M. Keel and T. Tao, Endpoint Strichartz estimates, American Journal of Mathematics, vol. 120, no. 5, pp. 955–980, 1998.10.1353/ajm.1998.0039Search in Google Scholar

5. C. Kenig and F. Merle, Global well-posedness, scattering and blow-up for the energy critical, focusing non-linear Schrödinger equation in the radial case, Inventiones mathematicae, vol. 166, no. 3, pp. 645– 675, 2006.10.1007/s00222-006-0011-4Search in Google Scholar

6. S. N. Bose, Plancks gesetz und lichtquantenhypothese, Zeitschrift für Physik, vol. 26, pp. 178–181, Dec 1924.10.1007/BF01327326Search in Google Scholar

7. A. Einstein, Quantentheorie des einatomigen idealen Gases. No. 2 in Sitzungsberichte der Preussischen Akademie der Wissenschaften. Physikalisch-mathematische Klasse, Verlag d. Akad. d. Wiss., 1924.Search in Google Scholar

8. T. Cazenave, Semilinear Schrödinger Equations. Courant lecture notes in mathematics, American Mathematical Society, 2003.10.1090/cln/010Search in Google Scholar

9. T. Cazenave and P. L. Lions, Orbital stability of standing waves for some nonlinear Schrödinger equations, Communications in Mathematical Physics, vol. 85, no. 4, pp. 549–561, 1982.10.1007/BF01403504Search in Google Scholar

10. V. E. Zakharov and B. Shabat, Exact theory of two–dimensional self–focusing and one–dimensional self–modulation of waves in nonlinear media, Journal of Experimental and Theoretical Physics, vol. 34, no. 1, pp. 62–71, 1972.Search in Google Scholar

11. R. Adami, C. Cacciapuoti, D. Finco, and D. Noja, On the structure of critical energy levels for the cubic focusing NLS on star graphs, Journal of Physics A: Mathematical and Theoretical, vol. 45, p. 192001, apr 2012.Search in Google Scholar

12. R. Adami, E. Serra, and P. Tilli, NLS ground states on graphs, Calculus of Variations and Partial Differential Equations, vol. 54, pp. 743–761, Sep 2015.10.1007/s00526-014-0804-zSearch in Google Scholar

13. S. Dovetta and L. Tentarelli, Ground states of the L2-critical NLS equation with localized nonlinearity on a tadpole graph, Operator Theory: Advances and Applications. to appear.Search in Google Scholar

14. J. L. Marzuola and D. E. Pelinovsky, Ground state on the dumbbell graph, Applied Mathematics Research eXpress, vol. 2016, no. 1, pp. 98–145, 2016.Search in Google Scholar

15. D. Noja, D. Pelinovsky, and G. Shaikhova, Bifurcations and stability of standing waves in the nonlinear Schrödinger equation on the tadpole graph, Nonlinearity, vol. 28, no. 7, pp. 2343–2378, 2015.Search in Google Scholar

16. C. Cacciapuoti, S. Dovetta, and E. Serra, Variational and stability properties of constant solutions to the NLS equation on compact metric graphs, Milan Journal of Mathematics, vol. 86, no. 2, pp. 305– 327, 2018.10.1007/s00032-018-0288-ySearch in Google Scholar

17. S. Dovetta, Existence of infinitely many stationary solutions of the L2–subcritical and critical NLSE on compact metric graphs, Journal of Differential Equations, vol. 264, no. 7, pp. 4806–4821, 2018.Search in Google Scholar

18. S. Dovetta and L. Tentarelli, L2–critical NLS on noncompact metric graphs with localized nonlinearity: topological and metric features, Calculus of Variations and Partial Differential Equations, 2019. to appear.10.1007/s00526-019-1565-5Search in Google Scholar

19. E. Serra and L. Tentarelli, Bound states of the NLS equation on metric graphs with localized nonlinearities, Journal of Differential Equations, vol. 260, no. 7, pp. 5627–5644, 2016.Search in Google Scholar

20. E. Serra and L. Tentarelli, On the lack of bound states for certain NLS equations on metric graphs, Nonlinear Analysis: Theory, Methods and Applications, vol. 145, pp. 68–82, 2016.10.1016/j.na.2016.07.008Search in Google Scholar

21. L. Tentarelli, NLS ground states on metric graphs with localized nonlinearities, Journal of Mathematical Analysis and Applications, vol. 433, no. 1, pp. 291–304, 2016.10.1016/j.jmaa.2015.07.065Search in Google Scholar

22. R. Adami, E. Serra, and P. Tilli, Negative energy ground states for the L2 -critical NLSE on metric graphs, Communications in Mathematical Physics, vol. 352, pp. 387–406, May 2017.10.1007/s00220-016-2797-2Search in Google Scholar

23. W. Borrelli, R. Carlone, and L. Tentarelli, Nonlinear Dirac equation on graphs with localized non- linearities: Bound states and nonrelativistic limit, SIAM Journal on Mathematical Analysis, vol. 51, pp. 1046–1081, 01 2019.Search in Google Scholar

24. W. Borrelli, R. Carlone, and L. Tentarelli, An overview on the standing waves of nonlinear Schrödinger and Dirac equations on metric graphs with localized nonlinearity, Symmetry, vol. 11, no. 2, 2019.10.3390/sym11020169Search in Google Scholar

25. S. Gilg, D. Pelinovsky, and G. Schneider, Validity of the NLS approximation for periodic quantum graphs, Nonlinear Differential Equations and Applications NoDEA, vol. 63, no. 6, p. 30, 2016.10.1007/s00030-016-0417-7Search in Google Scholar

26. A. Pankov, Nonlinear Schrödinger equations on periodic metric graphs, Discrete e Continuous Dynamical Systems, vol. 38, no. 2, pp. 697–714, 2018.10.3934/dcds.2018030Search in Google Scholar

27. D. Pelinovsky and G. Schneider, Bifurcations of standing localized waves on periodic graphs, Annales Henri Poincaré, vol. 18, no. 4, pp. 1185–1211, 2017.Search in Google Scholar

28. S. Dovetta, Mass-constrained ground states of the stationary NLSE on periodic metric graphs, Non- linear Differential Equations and Applications, 2019. to appear.10.1007/s00030-019-0576-4Search in Google Scholar

29. R. Adami, S. Dovetta, E. Serra, and P. Tilli, Dimensional crossover with a continuum of critical exponents for NLS on doubly periodic metric graphs, Analysis & PDE, vol. 12, pp. 1597–1612, 02 2019.Search in Google Scholar

30. R. Adami and S. Dovetta, One-dimensional versions of three-dimensional system: Ground states for the NLS on the spatial grid, Rendiconti di Matematica e delle sue Applicazioni, vol. 39, pp. 181–194, 2018.Search in Google Scholar

31. R. Adami, E. Serra, and P. Tilli, Threshold phenomena and existence results for NLS ground states on metric graphs, Journal of Functional Analysis, vol. 271, no. 1, pp. 201 – 223, 2016.10.1016/j.jfa.2016.04.004Search in Google Scholar

eISSN:
2038-0909
Idioma:
Inglés
Calendario de la edición:
Volume Open
Temas de la revista:
Mathematics, Numerical and Computational Mathematics, Applied Mathematics