|
|
|
|
References
|
|
| |
| 1. |
Bartsch T., Ding Y., “Solutions of nonlinear Dirac equations”, J. Differential Equations, 226 (2006), 210–249 |
| 2. |
Bartsch T., Ding Y., “On a nonlinear Schrödinger equation with periodic potential”, Math. Ann., 313 (1999), 15–37 |
| 3. |
Benci V., Rabinowitz P. H., “Critical point theorems for indefinite functionals”, Invent. Math., 52:3 (1979), 241–273 |
| 4. |
Boussaïd N., Comech A., Nonlinear Dirac equation. Spectral stability of solitary waves, Math. Surveys Monogr., 244, Amer. Math. Soc., Providence, RI, 2019 |
| 5. |
Boussaïd N., Comech A., “Spectral stability of small amplitude solitary waves of the Dirac equation with the Soler-type nonlinearity”, J. Funct. Anal., 277:12 (2019), 108829, 68 pp. |
| 6. |
Borrelli W., “Multiple solutions for a self-consistent Dirac equation in two dimensions”, J. Math. Phys., 59:4 (2018), 041503, 13 pp. |
| 7. |
Cavalcante M. P., Alves C., Medeiros E., “A semilinear Schrödinger equation with zero on the boundary of the spectrum and exponential growth in $\mathbb{R}^2$”, Commun. Contemp. Math., 21:6 (2019), 1850037, 21 pp. |
| 8. |
Chen P., Tang X., “Ground states for reaction-diffusion equations with spectrum point zero”, J. Geom. Anal., 32:12 (2022), 308, 34 pp. |
| 9. |
Comech A., Guan M., Gustafson S., “On linear instability of solitary waves for the nonlinear Dirac equation”, Ann. Inst. H. Poincaré C Anal. Non Linéaire, 31:3 (2014), 639–654 |
| 10. |
Cooper F., Khare A., Mihaila B., Saxena A., “Solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity”, Phys. Rev. E (3), 82:3 (2010), 036604, 14 pp. |
| 11. |
Ding Y., Variational methods for strongly indefinite problems, Interdis. Math. Sci., 7, World Sci. Publ. Co., Hackensack, NJ, 2007 |
| 12. |
Ding Y., Guo Q., Ruf B., “Stationary states of Dirac-Klein-Gordon systems with nonlinear interacting terms”, SIAM. J. Math. Anal., 53:5 (2021), 5731–5755 |
| 13. |
Ding Y., Guo Q., Yu Y., “Existence of semiclassical solutions for some critical Dirac equation”, J. Math. Phys., 62:1 (2021), 01150122, 22 pp. |
| 14. |
Esteban M., Séré E., “Stationary states of the nonlinear Dirac equation: a variational approach”, Comm. Math. Phys., 171:2 (1995), 323–350 |
| 15. |
Evequoz G, Weth T., “Dual variational methods and nonvanishing for the nonlinear Helmholtz equation”, Adv. Math., 280 (2015), 690–728 |
| 16. |
Finkelstein R., LeLevier R., Ruderman M., “Nonlinear spinor fields”, Phys. Rev. (2), 83:2 (1951), 326–332 |
| 17. |
Gutiérrez S., “Nontrivial $L^q$ solutions to the Ginzburg-Landau equation”, Math. Ann., 328:1-2 (2004), 1–25 |
| 18. |
Kryszewski W., Szulkin A., “Generalized linking theorem with an application to semilinear Schrödinger equation”, Adv. Differential Equations, 3:3 (1998), 441–472 |
| 19. |
Lions P. L., “The concentration-compactness principle in the calculus of variations. The locally compact case. II”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1:4 (1984), 223–284 |
| 20. |
Mederski J., “Solutions to a nonlinear Schrödinger equation with periodic potential and zero on the boundary of the spectrum”, Topol. Methods Nonlinear Anal., 46:2 (2015), 755–771 |
| 21. |
Ng W. K., Parwani R. R., “Nonlinear Dirac Equations”, Symmetry Integrability Geom. Methods Appl., 5 (2009), 023, 20 pp. |
| 22. |
Schechter M., “Nonlinear Schrödinger operators with zero in the spectrum”, Z. Angew. Math. Phys., 66:5 (2015), 2125–2141 |
| 23. |
Sun J., Chen H., Chu J., “On periodic Hamiltonian elliptic systems with spectrum point zero”, Math. Nachr., 285:17 (2012), 2233–2251 |
| 24. |
Wei Y., Yang M., “Existence of solutions for a system of diffusion equations with spectrum point zero”, Z. Angew. Math. Phys., 65:2 (2014), 325–337 |
| 25. |
Willem M., Zou W., “On a Schrödinger equation with periodic potential and spectrum point zero”, Indiana Univ. Math. J., 52:1 (2003), 109–132 |
| 26. |
Yang M., Chen W., Ding Y., “Solutions for periodic Schrödinger equation with spectrum zero and general superlinear nonlinearities”, J. Math. Anal. Appl., 364:2 (2010), 404–413 |