Open Access
Issue
ESAIM: COCV
Volume 32, 2026
Article Number 17
Number of page(s) 25
DOI https://doi.org/10.1051/cocv/2025098
Published online 10 March 2026
  1. Y. Sire and E. Valdinoci, Fractional Laplacian phase transitions and boundary reactions: a geometric inequality and a symmetry result. J. Funct. Anal. 256 (2009) 1842–1864 [Google Scholar]
  2. L. Caffarelli, J.-M. Roquejoffre and O. Savin, Nonlocal minimal surfaces. Commun. Pure Appl. Math. 63 (2010) 1111–1144 [CrossRef] [Google Scholar]
  3. L. Caffarelli and E. Valdinoci, Uniform estimates and limiting arguments for nonlocal minimal surfaces. Calc. Var. Part. Differ. Equ. 41 (2011) 203–240 [Google Scholar]
  4. C. Bucur, L. Lombardini and E. Valdinoci, Complete stickiness of nonlocal minimal surfaces for small values of the fractional parameter. Ann. Inst. H. Poincare C Anal. Non Linéaire 36 (2019) 655–703 [Google Scholar]
  5. S. Kumar, A. Kumar and Z.M. Odibat, A nonlinear fractional model to describe the population dynamics of two interacting species. Math. Methods Appl. Sci. 40 (2017) 4134–4148 [Google Scholar]
  6. Q.-Y. Guan and Z.-M. Ma, Boundary problems for fractional Laplacians. Stoch. Dyn. 5 (2005) 385–424 [Google Scholar]
  7. N. Laskin, Fractional quantum mechanics and Levy path integrals. Phys. Lett. A 268 (2000) 298–305 [Google Scholar]
  8. D. Applebaum, Levy processes—from probability to finance and quantum groups. Notices Amer. Math. Soc. 51 (2004) 1336–1347 [Google Scholar]
  9. I. Bialynicki-Birula and J. Mycielski, Wave equations with logarithmic nonlinearities. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astron. Phys. 23 (1975) 461–466 [Google Scholar]
  10. R. Carles and I. Gallagher, Universal dynamics for the defocusing logarithmic Schrodinger equation. Duke Math. J. 167 (2018) 1761–1801 [Google Scholar]
  11. T. Cazenave, Semilinear Schrodinger equations, vol. 10 of Courant Lecture Notes in Mathematics. New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI (2003). [Google Scholar]
  12. T. Cazenave, Stable solutions of the logarithmic Schrodinger equation. Nonlinear Anal. 7 (1983) 1127–1140 [Google Scholar]
  13. T. Cazenave and P.-L. Lions, Orbital stability of standing waves for some nonlinear Schrodinger equations. Commun. Math. Phys. 85 (1982) 549–561 [Google Scholar]
  14. A.H. Ardila, Existence and stability of standing waves for nonlinear fractional Schrodinger equation with logarithmic nonlinearity. Nonlinear Anal. 155 (2017) 52–64 [Google Scholar]
  15. T. Bartsch and Z.-Q. Wang, Multiple positive solutions for a nonlinear Schrödinger equation. Z. Angew. Math. Phys. 51 (2000) 366–384 [Google Scholar]
  16. M. Clapp and Y. Ding, Minimal nodal solutions of a Schröodinger equation with critical nonlinearity and symmetric potential. Differ. Integral Eq. 16 (2003) 981–992 [Google Scholar]
  17. C.O. Alves, G. Molica Bisci and I.S. da Silva, New minimax theorems for lower semicontinuous functions and applications. ESAIM: COCV 31 (2025) Art. no. 10. [Google Scholar]
  18. Z. Wang and H.-S. Zhou, Positive solutions for nonlinear Schröodinger equations with deepening potential well. J. Eur. Math. Soc. 11 (2009) 545–573 [Google Scholar]
  19. F.A. van Heerden and Z.-Q. Wang, Schrodinger type equations with asymptotically linear nonlinearities. Differ. Integral Equ. 16 (2003) 257–280 [Google Scholar]
  20. Z. Shen, F. Gao and M. Yang, On critical Choquard equation with potential well. Discrete Contin. Dyn. Syst. 38 (2018) 3567–3593 [Google Scholar]
  21. T. Bartsch, A. Pankov and Z.-Q. Wang, Nonlinear Schröodinger equations with steep potential well. Commun. Contemp. Math. 3 (2001) 549–569 [Google Scholar]
  22. M. Squassina and A. Szulkin, Multiple solutions to logarithmic Schroödinger equations with periodic potential. Calc. Var. Part. Differ. Equ. 54 (2015) 585–597 [Google Scholar]
  23. K. Tanaka and C. Zhang, Multi-bump solutions for logarithmic Schrodinger equations. Calc. Var. Part. Differ. Equ. 56 (2017) Paper No. 33, 35. [Google Scholar]
  24. C. Ji and A. Szulkin, A logarithmic Schröodinger equation with asymptotic conditions on the potential. J. Math. Anal. Appl. 437 (2016) 241–254 [Google Scholar]
  25. C.O. Alves and C. Ji, Multi-bump positive solutions for a logarithmic Schröodinger equation with deepening potential well. Sci. China Math. 65 (2022) 1577–1598 [Google Scholar]
  26. P. d'Avenia, M. Squassina and M. Zenari, Fractional logarithmic Schrödinger equations. Math. Methods Appl. Sci. 38 (2015) 5207–5216 [Google Scholar]
  27. Q. Li, S. Peng and W. Shuai, On fractional logarithmic Schrodinger equations. Adv. Nonlinear Stud. 22 (2022) 41–66 [Google Scholar]
  28. W. Shuai, Multiple solutions for logarithmic Schrodinger equations. Nonlinearity 32 (2019) 2201–2225 [Google Scholar]
  29. C. Zhang and X. Zhang, Bound states for logarithmic Schrodinger equations with potentials unbounded below. Calc. Var. Part. Differ. Equ. 59 (2020) Paper No. 23, 31. [Google Scholar]
  30. C.O. Alves, D.C. de Morais Filho and G.M. Figueiredo, On concentration of solution to a Schrödinger logarithmic equation with deepening potential well. Math. Methods Appl. Sci. 42 (2019) 4862–4875 [Google Scholar]
  31. T. Weth, Energy bounds for entire nodal solutions of autonomous superlinear equations. Calc. Var. Part. Differ. Equ. 27 (2006) 421–437 [Google Scholar]
  32. Y. Deng and W. Shuai, Sign-changing solutions for non-local elliptic equations involving the fractional Laplacian. Adv. Differ. Equ. 23 (2018) 109–134 [Google Scholar]
  33. A. Cotsiolis and N.K. Tavoularis, On logarithmic Sobolev inequalities for higher order fractional derivatives. C. R. Math. Acad. Sci. Paris 340 (2005) 205–208 [Google Scholar]
  34. Z.-Q. Wang and C. Zhang, Convergence from power-law to logarithm-law in nonlinear scalar field equations. Arch. Ration. Mech. Anal. 231 (2019) 45–61 [Google Scholar]
  35. A. Szulkin, Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems. Ann. Inst. H. Poincare Anal. Non Linéaire 3 (1986) 77–109 [Google Scholar]
  36. C. Cowan and A. Moameni, On supercritical elliptic problems: existence, multiplicity of positive and symmetry breaking solutions. Math. Ann. 389 (2024) 1731–1794 [Google Scholar]
  37. R. Song and Z. Vondracek, Potential theory of subordinate killed Brownian motion in a domain. Probab. Theory Related Fields 125 (2003) 578–592 [Google Scholar]
  38. R. Servadei and E. Valdinoci, Mountain pass solutions for non-local elliptic operators. J. Math. Anal. Appl. 389 (2012) 887–898 [Google Scholar]
  39. E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker's guide to the fractional Sobolev spaces. Bull. Sci. Math. 136 (2012) 521–573 [Google Scholar]
  40. M. Willem, Minimax theorems, vol. 24 of Progress in Nonlinear Differential Equations and their Applications. Birkhöauser Boston, Inc., Boston, MA (1996). [Google Scholar]
  41. C.O. Alves and D.C. de Morais Filho, Existence and concentration of positive solutions for a Schrödinger logarithmic equation. Z. Angew. Math. Phys. 69 (2018) Paper No. 144, 22. [Google Scholar]
  42. X. He and W. Zou, Multiplicity of concentrating solutions for a class of fractional kirchhoff equation. Manuscripta Math. 158 (2019) 159–203 [Google Scholar]
  43. A. Marino and D. Mugnai, Asymptotically critical points and their multiplicity. Topol. Methods Nonlinear Anal. 19 (2001) 29–38 [Google Scholar]
  44. A. Marino and D. Mugnai, Asymptotical multiplicity and some reversed variational inequalities. Topol. Methods Nonlinear Anal. 20 (2002) 43–62 [Google Scholar]

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