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All issues Volume 31 (2025) ESAIM: COCV, 31 (2025) 10 References
Open Access
Issue
ESAIM: COCV
Volume 31, 2025
Article Number 10
Number of page(s) 43
DOI https://doi.org/10.1051/cocv/2024005
Published online 10 February 2025
  1. T. Bartsch, Infinitely many solutions of a symmetric Dirichlet problem. Nonlinear Anal. TMA 20 (1993) 1205–1216. [CrossRef] [Google Scholar]
  2. M. Willem, Minimax Theorems. Birkhäuser, Boston (1996). [CrossRef] [Google Scholar]
  3. T. Bartsch and M. Willem, On an elliptic equation with concave and convex nonlinearities. Proc. Amer. Math. Soc. 123 (1995) 3555–3561. [CrossRef] [MathSciNet] [Google Scholar]
  4. C.J. Batkam, and F. Colin, Generalized Fountain Theorem and applications to strongly indefinite semilinear problems. J. Math. Anal. Appl. 405 (2013) 438–452. [CrossRef] [MathSciNet] [Google Scholar]
  5. W. Kryszewski and A. Szulkin, Generalized linking theorem with an application to a semilinear Schrödinger equation. Adv. Diff. Equ. 3 (1998) 441–472. [Google Scholar]
  6. S. Chen and C. Wang, An infinite-dimensional linking theorem without upper semi-continuous assumption and its applications. J. Math. Anal. Appl. 420 (2014) 1552–1567. [CrossRef] [MathSciNet] [Google Scholar]
  7. L. Gu and H. Zhou, An improved fountain theorem and its application. Adv. Nonlinear Stud. 17 (2016) 727–738. [Google Scholar]
  8. W. Zou, Variant fountain theorems and their applications. Manuscripta Math. 104 (2001) 343–358. [CrossRef] [MathSciNet] [Google Scholar]
  9. D. Liu, On a p-Kirchhoff equation via Fountain Theorem and Dual Fountain Theorem. Nonlinear Anal. 72 (2010) 302–308. [CrossRef] [MathSciNet] [Google Scholar]
  10. J. Sun, Infinitely many solutions for a class of sublinear Schrödinger–Maxwell equations. J. Math. Anal. Appl. 390 (2012) 514–522. [CrossRef] [MathSciNet] [Google Scholar]
  11. F.H. Clarke, Optimization and Nonsmooth Analysis. Wiley, New York (1983). [Google Scholar]
  12. K.C. Chang, Variational methods for nondifferentiable functionals and their applications to partial differential equations. J. Math. Anal. Appl. 80 (1981) 102–129. [CrossRef] [MathSciNet] [Google Scholar]
  13. P.H. Rabinowitz, Minimax Methods in Critical Point Theory with Application to Differential Equations. American Mathematical Society, CBMS, 65, USA (1986). [CrossRef] [Google Scholar]
  14. S. Carl, V.K. Le and D. Motreanu, Nonsmooth Variational Problems and Their Inequalities: Comparison Principles and Applications. Springer, New York (2007). [CrossRef] [Google Scholar]
  15. D. Motreanu and P.D. Panagiotopoulos, Minimax Theorems and Qualitative Properties of The Solutions of Hemivariational Inequalities. Springer Science + Business Media Dordrecht (1999). [CrossRef] [Google Scholar]
  16. A. Szulkin, Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems. Ann. Inst. H. Poincaré Anal. Non Linéaire 3 (1986) 77–109. [CrossRef] [MathSciNet] [Google Scholar]
  17. 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) 144–165. [CrossRef] [Google Scholar]
  18. C.O. Alves and C. Ji, Existence and concentration of positive solutions for a logarithmic Schrödinger equation via penalization method. Calc. Var. 59 (2020) 21. [CrossRef] [Google Scholar]
  19. C. Ji and A. Szulkin, A logarithmic Schroodinger equation with asymptotic conditions on the potential. J. Math. Anal. Appl. 437 (2016) 241–254. [CrossRef] [MathSciNet] [Google Scholar]
  20. J. Kobayashi and M. Ôtani, The principle of symmetric criticality for non-differentiable mappings. J. Funct. Anal. 214 (2004) 428–449. [CrossRef] [MathSciNet] [Google Scholar]
  21. G. Mancini and Musina, Hole and obstacles. Ann. Inst. H. Poincaré Anal. Non Linéaire 4 (1988) 323–345. [CrossRef] [MathSciNet] [Google Scholar]
  22. M. Squassina and A. Szulkin, Multiple solution to logarithmic Schrödinger equations with periodic potential. Calc. Var. 54 (2015) 585–597. [CrossRef] [MathSciNet] [Google Scholar]
  23. G. Dai, Nonsmooth version of Fountain theorem and its application to a Dirichlet-type differential inclusion problem. Nonlinear Anal. 72 (2010) 1454–1461. [CrossRef] [MathSciNet] [Google Scholar]
  24. H. Heinz, Free Ljusternik–Schnirelman theory and the bifurcation diagrams of certain singular nonlinear problems. J. Diff. Equ. 66 (1987) 263–300. [CrossRef] [Google Scholar]
  25. D.C. Clark, A variant of the Ljusternik–Schnirelman theory. Indiana Univ. Math. J. 22 (1972) 65–74. [Google Scholar]
  26. B. Kawohl and F. Schuricht, Dirichlet problems for the 1-Laplace operator, including the eigenvalue problem. Commun. Contemp. Math. 9 (2007) 525–543. [Google Scholar]
  27. C.O. Alves, G.M. Figueiredo and M.T.O. Pimenta, Existence and profile of ground-state solutions to a 1-Laplacian problem in ℝN. Bull. Braz. Math. Soc., New Series, doi:10.1007/s00574-019-00179-4 [Google Scholar]
  28. C.O. Alves and M.T.O. Pimenta, On existence and concentration of solutions to a class of quasilinear problems involving the 1-Laplace operator. Calc. Var. 56 (2017) 143. [CrossRef] [Google Scholar]
  29. M. Degiovanni and P. Magrone, Linking solutions for quasilinear equations at critical growth involving the 1-Laplace operator. Calc. Var. 36 (2009) 591–609. [CrossRef] [MathSciNet] [Google Scholar]
  30. G.M. Figueiredo and M.T.O. Pimenta, Strauss’ and Lions’ type results in BV (ℝN) with an application to 1-Laplacian problem. Milan J. Math. 86 (2018) 15–30. [CrossRef] [MathSciNet] [Google Scholar]
  31. G.M. Figueiredo and M.T.O. Pimenta, Existence of bounded variation solutions for a 1-Laplacian problem with vanishing potentials. J. Math. Anal. Appl. 459 (2018) 861–878. [CrossRef] [MathSciNet] [Google Scholar]
  32. K. Chang, The spectrum of the 1-Laplace operator. Commun. Contemp. Math. 9 (2009) 515–543. [Google Scholar]
  33. F. Demengel, On some nonlinear partial differential equations involving the 1-Laplacian and critical Sobolev exponent. ESAIM Control Optim. Calc. Var. 4 (1999) 667–686. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  34. A. Molino Salas and S. Segura de León, Elliptic equations involving the 1-Laplacian and a subcritical source term. Nonlinear Anal. 168 (2018) 50–66. [CrossRef] [MathSciNet] [Google Scholar]
  35. J.C. Ortiz Chata and M.T.O. Pimenta, A Berestycki-Lions’ type result to a quasilinear elliptic problem involving the 1-laplacian operator. J. Math. Anal. Appl., doi.org/10.1016/j.jmaa.2021.125074. [Google Scholar]
  36. I. Ekeland, Nonconvex minimization problems. Bull. Amer. Math. Soc. (1979) 443–474. [CrossRef] [MathSciNet] [Google Scholar]
  37. G. Molica Bisci and P. Pucci, Nonlinear Problems with Lack of Compactness, De Gruyter Series in Nonlinear Analysis and Applications, Vol. 36 (2021). [CrossRef] [Google Scholar]
  38. F.H. Clarke, Generalized gradients and applications. Trans. Amer. Math. Soc. 205 (1975) 247–262. [CrossRef] [MathSciNet] [Google Scholar]
  39. T. Bartsch, Topological Methods for Variational Problems with Symmetries, Lectures Notes in Math. 1560, Springer (1993). [Google Scholar]
  40. L. Nachbin, The Haar Integral. D. Van Nostrand Company, Canada (1965). [Google Scholar]
  41. L.C. Evans, Partial Differential Equations. American Mathematical Society, USA (1998). [Google Scholar]
  42. C. Bereanu and P. Jebelean, Multiple critical points for a class of periodic lower semicontinuous functionals. Discrete Contin. Dyn. Syst. 33 (2013) 47–66. [CrossRef] [MathSciNet] [Google Scholar]
  43. C.O. Alves, J.V. Gonçalves and J.A. Santos, Strongly nonlinear multivalued elliptic equations on a bounded domain. J. Glob. Optim. 58 (2014) 565–593. [CrossRef] [Google Scholar]
  44. J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I. Springer, Berlin (1977). [CrossRef] [Google Scholar]
  45. I. Peral Alonso, Multiplicity of solutions for the p-laplacian. Second School of Nonlinear Functional Analysis and Applications to Differential Equations, Trieste (1997). [Google Scholar]
  46. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford University Press, Oxford (2000). [Google Scholar]
  47. H. Attouch, G. Buttazzo and G. Michaille, Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization. MPS-SIAM, Philadelphia (2006). [CrossRef] [Google Scholar]

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