Autor

DOI:

https://doi.org/10.12775/TMNA.2021.055

Słowa kluczowe

Abstrakt

Bibliografia

T. Aubin, Sur la fonction exponentielle, C.R. Acad. Sci. Paris Sér. A–B 270 (1970), A1514–A1516.

L. Battaglia, A. Jevnikar, A. Malchiodi and D. Ruiz, A general existence result for the Toda system on compact surfaces, Adv. Math. 285 (2015), 937–979.

A. Caffarelli and Y. S. Yang, Vortex condensation in the Chern–Simons Higgs model: An existence theorem, Comm. Math. Phys. 168 (1995), 321–336.

J. Castéras, A mean field type flow part I: compactness of solutions to a perturbed mean field type equation, Calc. Var. Partial. Differ. Equ. 53 (2015), 221–246.

J. Castéras, A mean field type flow part II:existence and convergence, Pacific J. Math. 276 (2015), 321–345.

A. Chang and P. Yang, Prescribing Gaussian curvature on S 2 , Acta Math. 159 (1987), 215–259.

A. Chang and P. Yang, Conformal deformation of metrics on S 2 , J. Differ. Geom. 23 (1988), 259–296.

W. Chen and C. Li, Prescribing Gaussian curvatures on surfaces with conical singularities, J. Geom. Anal. 1 (1991), 359–372.

C. Chen and C. Lin, Sharp estimates for solutions of multi-bubbles in compact Riemann surfaces, Comm. Pure Appl. Math. 55 (2002), 728–771.

C. Chen and C. Lin, Topological degree for a mean field equation on Riemann surfaces, Comm. Pure Appl. Math. 56 (2003), 1667–1727.

P. Cherrier, Une inégalité de Sobolev sur les variétés Riemanniennes, Bull. Sci. Math. 103 (1979), 353–374.

W. Ding, J. Jost, J. Li and G. Wang, The differential equation ∆u = 8π − 8πheu on a compact Riemann surface, Asian J. Math. 1 (1997), 230–248.

W. Ding, J. Jost, J. Li and G. Wang, Existence results for mean field equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999), 653–666.

Z. Djadli, Existence result for the mean field problem on Riemann surfaces of all genuses, Commun. Contemp. Math. 10 (2008), 205–220.

Z. Djadli and A. Malchiodi, Existence of conformal metrics with constant Q-curvature, Ann. of Math. 168 (2008), 813–858.

L. Fontana, Sharp borderline Sobolev inequalities on compact Riemannian manifolds, Comment. Math. Helv. 68 (1993), 415–454.

J. Kazdan and F. Warner, Curvature functions for compact 2-manifolds, Ann. Math. 99 (1974), 14–47.

J. Li and C. Zhu, The convergence of the mean field type flow at a critical case, Calc. Var. Partial Differential Equations 58 (2019), 60–78.

Y. Li, Harnack type inequality: the method of moving planes, Comm. Math. Phys. 200 (1999), 421–444.

C. Lin, Topological degree for mean field equations on S 2 , Duke Math. J. 104 (2000), 501–536.

A. Malchiodi and C.B. Ndiaye, Some existence results for the Toda system on closed surfaces, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 18 (2007), 391–412.

A. Malchiodi, Topological methods for an elliptic equation with exponential nonlinearities, Discrete Contin. Dyn. Syst. 21 (2008), 277–294.

J. Moser, A sharp form of an inequality by N. Trudinger, Indiana Univ. Math. J. 20 (1971), 1077–1091.

J. Moser, On a nonlinear problem in differential geometry, Dynamical systems (Proc. Sympos., Univ. Bahia, Salvador, 1971), Academic Press, New York, 1973, pp. 273–280.

M. Nolasco and G. Tarantello, On a sharp Sobolev-type inequality on two-dimensional compact manifolds, Arch. Ration. Mech. Anal. 145 (1998), 161–195.

M. Struwe, The existence of surfaces of constant mean curvature with free boundaries, Acta Math. 160 (1988), 19–64.

M. Struwe and G. Tarantello, On multivortex solutions in Chern–Simons gauge theory, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 1 (1998), 109–121.

L. Sun, Y. Wang and Y. Yang, Existence results for a generalized mean field equation on a closed Riemann surface, (2021), arXiv: 2101.03859.

L. Sun and J. Zhu, Global existence and convergence of a flow to Kazdan–Warner equation with non-negative prescribed function, Calc. Var. Partial Differential Equations 60 (2021), paper no. 42, 26 pp.

L. Sun and J. Zhu, Existence of Kazdan–Warner equation with sign-changing prescribed function, (2021), arXiv: 2012.12840.

G. Tarantello, Multiple condensate solutions for the Chern–Simons–Higgs theory, J. Math. Phys. 37 (1996), 3769–3796.

M. Wang and Q. Liu, The equation ∆u + ∇φ · ∇u = 8πc(1 − heu ) on a Riemann surface, J. Partial Differ. Equ. 25 (2012), 335–355.

Y.S. Yang, Solitons in Field Theory and Nonlinear Analysis, Springer Monographs in Mathematics, Springer–Verlag, New York, 2001.

Y. Yang, Extremal functions for Trudinger–Moser inequalities of Adimurthi–Druet type in dimension two, J. Differential Equations 258 (2015), 3161–3193.

Y. Yang, and X. Zhu, A remark on a result of Ding–Jost-Li–Wang, Proc. Amer. Math. Soc. 145 (2017), 3953–3959.

Y. Yang and X. Zhu, Existence of solutions to a class of Kazdan–Warner equations on compact Riemannian surface, Sci. China Math. 61 (2018), 1109–1128.

M. Zhang, A Trudinger–Moser inequality involving Lp -norm on a closed Riemann surface, Acta Math. Sin. (Engl. Ser.) 37 (2021), 538–550.

M. Zhang, Extremal functions for a class of trace Trudinger–Moser inequalities on a compact Riemann surface with smooth boundary, Commun. Pure Appl. Anal. 20 (2021), 1721–1735.

Opublikowane

2022-08-31

Jak cytować

1.
& . Topological Methods in Nonlinear Analysis [online]. 31 sierpień 2022, T. 60, nr 1, s. 267–285. [udostępniono 22.7.2024]. DOI 10.12775/TMNA.2021.055.

Numer

Dział

Articles

Statystyki

Liczba wyświetleń i pobrań: 0
Liczba cytowań: 0