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All issues Volume 59 / No 2 (March-April 2025) ESAIM: M2AN, 59 2 (2025) 899-923 References
Open Access
Issue
ESAIM: M2AN
Volume 59, Number 2, March-April 2025
Page(s) 899 - 923
DOI https://doi.org/10.1051/m2an/2025009
Published online 02 April 2025
  1. A. Ambrosetti and A. Malchiodi, Perturbation Methods and Semilinear Elliptic Problems on Rn. Birkh¨auser, Basel (2006). [Google Scholar]
  2. A. Ambrosetti and A. Malchiodi, Nonlinear Analysis and Semilinear Elliptic Problems. Cambridge University Press, Cambridge (2007). [Google Scholar]
  3. W. Ao, M. Musso, F. Pacard and J. Wei, Solutions without any symmetry for semilinear elliptic problems. J. Funct. Anal. 270 (2016) 884–956. [Google Scholar]
  4. W. Bao and Q. Du, Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow. SIAM J. Sci. Comput. 25 (2004) 1674–1697. [CrossRef] [MathSciNet] [Google Scholar]
  5. T. Bartsch and M. Willem, Infinitely many radial solutions of a semilinear elliptic problem on RN. Arch. Ration. Mech. Anal. 124 (1993) 261–276. [Google Scholar]
  6. H. Berestycki and P.-L. Lions, Nonlinear scalar field equations. I. Existence of a ground state. Arch. Ration. Mech. Anal. 82 (1983) 313–345. [Google Scholar]
  7. H. Berestycki and P.-L. Lions, Nonlinear scalar field equations. II. Existence of infinitely many solutions. Arch. Ration. Mech. Anal. 82 (1983) 347–375. [Google Scholar]
  8. H. Berestycki, T. Gallouët and O. Kavian, Équations de champs scalaires euclidiens non linéaires dans le plan. C. R. Acad. Sci. Paris 297 (1983) 307–310. [Google Scholar]
  9. C. Besse, R. Duboscq and S. Le Coz, Gradient flow approach to the calculation of stationary states on nonlinear quantum graphs. Ann. Henri Lebesgue 5 (2022) 387–428. [Google Scholar]
  10. C. Besse, R. Duboscq and S. Le Coz, Numerical simulations on nonlinear quantum graphs with the GraFiDi library. SMAI J. Comput. Math. 8 (2022) 1–47. [Google Scholar]
  11. D. Bonheure, V. Bouchez, C. Grumiau and J. van Schaftingen, Asymptotics and symmetries of least energy nodal solutions of Lane–Emden problems with slow growth. Commun. Contemp. Math. 10 (2008) 609–631. [MathSciNet] [Google Scholar]
  12. T. Cazenave, Semilinear Schrödinger Equations. Vol. 10 of Courant Lecture Notes in Mathematics. New York University/Courant Institute of Mathematical Sciences, New York (2003). [Google Scholar]
  13. Y.S. Choi and P.J. McKenna, A mountain pass method for the numerical solution of semilinear elliptic problems. Nonlinear Anal. Theory Methods Appl. 20 (1993) 417–437. [Google Scholar]
  14. C. Cortázar, M. García-Huidobro and C.S. Yarur, On the uniqueness of the second bound state solution of a semilinear equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009) 2091–2110. [Google Scholar]
  15. C. Cortázar, M. García-Huidobro and C.S. Yarur, On the uniqueness of sign changing bound state solutions of a semilinear equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 28 (2011) 599–621. [Google Scholar]
  16. D.G. Costa, Z. Ding and J.M. Neuberger, A numerical investigation of sign-changing solutions to superlinear elliptic equations on symmetric domains. J. Comput. Appl. Math. 131 (2001) 299–319. [Google Scholar]
  17. G. Fibich, The Nonlinear Schrödinger Equation. Vol. 192 of Applied Mathematical Sciences. Springer, Cham (2015). [Google Scholar]
  18. M. Ghimenti and J. Van Schaftingen, Nodal solutions for the Choquard equation. J. Funct. Anal. 271 (2016) 107–135. [Google Scholar]
  19. B. Gidas, W.M. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle. Commun. Math. Phys. 68 (1979) 209–243. [Google Scholar]
  20. I. Ianni, Sign-changing radial solutions for the Schrödinger–Poisson–Slater problem. Topol. Methods Nonlinear Anal. 41 (2013) 365–385. [Google Scholar]
  21. M.K. Kwong, Uniqueness of positive solutions of Δu − u + up = 0 in Rn. Arch. Ration. Mech. Anal. 105 (1989) 243–266. [Google Scholar]
  22. P.-L. Lions, Solutions complexes d’équations elliptiques semilinéaires dans RN. C. R. Acad. Sci. Paris Sér. I Math. 302 (1986) 673–676. [Google Scholar]
  23. L.A. Maia, D. Raom, R. Ruviaro and Y.D. Sobral, Mini-max algorithm via Pohozaev manifold. Nonlinearity 34 (2021) 642–668. [Google Scholar]
  24. W.A. Strauss, Existence of solitary waves in higher dimensions. Comm. Math. Phys. 55 (1977) 149–162. [MathSciNet] [Google Scholar]
  25. C. Sulem and P.-L. Sulem, The Nonlinear Schrödinger Equation: Self-focusing and Wave Collapse. Vol. 139 of Applied Mathematical Sciences. Springer-Verlag, New York (1999). [Google Scholar]
  26. A. Szulkin and T. Weth, The method of Nehari manifold, in Handbook of Nonconvex Analysis and Applications. Int. Press, Somerville, MA (2010) 597–632. [Google Scholar]
  27. M. Tang, Uniqueness of bound states to Δu − u + |u|p −1u = 0 in Rn, n ≥ 3. Preprint: arXiv:2409.06915 (2024). [Google Scholar]
  28. M. Willem, Minimax Theorems. Progress in Nonlinear Differential Equations and their Applications, 24. Birkh¨auser Boston, Inc., Boston, MA (1996). [Google Scholar]

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