Citation: |
[1] |
D. Bartolucci, C.C. Chen, C.S. Lin and G. Tarantello:, Profile of blow-up solutions to mean field equations with singular data, Comm. Partial Differential Equations 29 no. 7-8 (2004), 1241-1265. |
[2] |
D. Bartolucci, and G. Tarantello:, The Liouville equation with singular data: a concentration-compactness principle via a local representation formula, J. Differential Equations 185 (2002), 161-180. |
[3] |
D. Bartolucci, and G. Tarantello:, Liouville type equations with singular data and their applications to periodic multivortices for the Electroweak Theory, Comm. Math. Pfys. 229 (2002), 3-47. |
[4] |
H. Brezis, and F. Merle:, Uniform estimates and blow-up behavior for solutions of $-\Delta u = V(x)e^u$ in two dimensions, Comm. Partial Differential Equations 16 (1991), 1223-1253. |
[5] |
P. Esposito:, A Class of Liouville-Type Equations Arising in Chern-Simons Vortex Theory: Asymptotics and Construction of Blowing Up Solutions, Ph. D. thesis, Universitá degli Studi Roma "Tor Vergata", Roma, Italy, 2003. |
[6] |
P. Esposito:, Blowup solutions for a Liouville equation with singular data, SIAM. J. Math. Anal. 36 (2005), 1310-1345. |
[7] |
P. Esposito:, Blowup solutions for a Liouville equation with singular data, in Proceedings of the International Conference " Recent Advances in Elliptic and Parabolic Problems" (C.C. Chen, M. Chipot, C.S. Lin (ed.)), World Scientific, (2005), 61-79. |
[8] |
Y. Y. Li, and I. Shafrir:, Blow-up analysis for solutions of $-\Delta u = V e^u$ in dimension two, Indiana Univ. Math. J. 43 (1994), 1255-1270. |
[9] |
L. Ma, and J. Wei:, Convergence for a Liouville equation, Comment. Math. Helv. 76 (2001), 506-514. |
[10] |
K. Nagasaki, and T. Suzuki:, Asymptotic analysis for two-dimensional elliptic eigenvalue problems with exponentially dominated nonlinearities, Asymptotic Anal. 3 (1990), 173-188. |
[11] |
J. Prajapat, and G. Tarantello:, On a class of elliptic problems in $\mathbbR^2$: symmetry and uniqueness results, Proc. Roy. Soc. Edinburgh 131 A (2001), 967-985. |
[12] |
F. Takahashi:, Blow up points and the Morse indices of solutions to the Liouville equation in two-dimension, Advances in Nonlinear Stud. 12 no.1, (2012), 115-122. |
[13] |
F. Takahashi:, Blow up points and the Morse indices of solutions to the Liouville equation : inhomogeneous case, submitted. |
[14] |
G. Tarantello:, " Selfdual Gauge Field Vortices: An Analytical Approach," Progress in Nonlinear Differential Equations and Their Applications 72, Birkhäuser, Boston (2008) |
[15] |
Y. Yang:, "Solitons in Field Theory and Nonlinear Analysis," Springer Monographs in Mathematics, Springer-Verlag, New York (2001) |