[1]
|
N. D. Alikakos, “Some Basic Facts on the System ,” Procceedings of the American Mathematical Society, Vol. 139, No. 1, January 2011, pp. 153-162. doi:10.1090/S0002-9939-2010-10453-7
|
[2]
|
F. Bethuel, P. Gravejat and J.-C. Saut, “Traveling Waves for the Gross-Pitaevskii Equation II,” Communications in Mathemati-cal Physics, Vol. 285, No. 2, 2009, pp. 567-651. doi:10.1007/s00220-008-0614-2
|
[3]
|
H. Brezis, “Comments on Two Notes by L. Ma and X. Xu,” Comptes Rendus Mathematique, 2011.
|
[4]
|
A. Chaljub-Simon and Y. Cho-quet-Bruhat, “Global Solutions of the Lichnerowicz Equation in General Relativity on an Asymptotically Euclidean Com-plete Manifold,” General Relativity and Gravitation, Vol. 12, No. 2, 1980, pp. 175-185. doi:10.1007/BF00756471
|
[5]
|
F. Bethuel, H. Brezis and F. Helein, “Ginzburg-Landau Vortices,” Birkhauser, Basel and Boston, 1994.
|
[6]
|
W. X. Chen and C. M. Li, “An Integral System and the Lane-Emden Conjecture,” Discrete Continuous Dynamical Systems, Vol. 24, No. 4, 2009, pp. 1167-1184.
doi:10.3934/dcds.2009.24.1167
|
[7]
|
Y. Choquet-Bruhat, J. Isenberg and D. Pollack, “The Einstein-Scalar Field Constraints on Asymptotically Euclidean Manifolds,” Chinese Annals of Mathematics, Series B, Vol. 27, No. 1, 2006, pp. 31-52.
doi:10.1007/s11401-005-0280-z
|
[8]
|
Y. Choquet-Bruhat, J. Isenberg and D. Pollack, “The Constraint Equations for the Einstein-Scalar Field System on Compact Manifolds,” Classi-cal and Quantum Gravity, Vol. 24, No. 4, 2007, pp. 809-828.
doi:10.1088/0264-9381/24/4/004
|
[9]
|
Y. H. Du and L. Ma, “Logistic Equations on by a Squeezing Method Involving Boundary Blow-up Solutions,” Journal of London Mathemati-cal Society, Vol. 64, No. 2, 2001, pp. 107-124.
doi:10.1017/S0024610701002289
|
[10]
|
A. Farina. “Fi-nite-Energy Solutions, Quantization Effects and Liouville-Type Results for a Variant of the Ginzburg -Landau Systems in RK,” Comptes rendus de l'Académie des Sciences, Série 1, Mathé-matique, Vol. 325, No. 5, 1997, pp. 487-491
|
[11]
|
E. Hebey, F. Pacard and D. Pollack, “A Variational Analysis of Ein-stein-Scalar Field Lichnerowicz Equations on Compact Rie-mannian Manifolds,” Communications in Mathematical Phys-ics, Vol. 278, No. 1, 2008, pp. 117-132. doi:10.1007/s00220-007-0377-1
|
[12]
|
E. Hebey, “Existence, Stability and Instability for Einstein-Scalar Field Lichnerowicz Equations,” Two hours lectures, Institute for Advanced Study, Princeton, October 2008.
|
[13]
|
J. Davila, “Global Regularity for a Singular Equation and Local Minimizers of a Nondiffer-entiable Functional,” Communications in Contemporary Mathematics, Vol. 6, No. 1, 2004, pp. 165-193.
doi:10.1142/S0219199704001240
|
[14]
|
F. H. Lin, “Static and Moving Vortices in Ginzburg-Landau Theories,” In: T. N. Knoxville, Ed., Nonlinear Partial Differential Equations in Geometry and Physics, Progress in Nonlinear Differential Equations and their Applications, Birkh?user, Basel, Vol. 29, 1997, pp. 71-111.
|
[15]
|
F. H. Lin and J. C. Wei, “Traveling Wave Solutions of the Schrodinger Map Equation,” Communi-cations on Pure and Applied Mathematics, Vol. 63, No. 12, 2010, pp. 1585-1621. doi:10.1002/cpa.20338
|
[16]
|
L. Ma, “Liouville Type Theorem and Uniform Bound for the Lichnerowicz Equation and the Ginzburg-Landau Equation,” Comptes Rendus Mathematique, Vol. 348, No. 17, 2010, pp. 993-996. doi:10.1016/j.crma.2010.07.031
|
[17]
|
L. Ma, “Three Remarks on Mean Field Equations,” Pacific Journal of Mathematics, Vol. 242, No. 1, 2009, pp. 167-171. doi:10.2140/pjm.2009.242.167
|
[18]
|
L. Ma and X. W. Xu, “Uniform Bound and a Non-Existence Result for Lichnerowicz Equation in the Whole N-Space,” Comptes Rendus Mathe-matique, Vol. 347, No. 13-14, 2009, pp. 805-808.
doi:10.1016/j.crma.2009.04.017
|
[19]
|
L. Modica, “Monotonic-ity of the Energy for Entire Solutions of Semilinear Elliptic Equations,” In: F. Colombini, A. Marino and L. Modica, Eds., Partial Differential Equations and the Calculus of Variations, Birkhauser, Boston, Vol. 2, 1989, pp. 843-850.
|
[20]
|
E. Sandier and S. Serfaty., “Vortices in the Magnetic Ginzburg-Landau Model,” Birkhauser, Basel, 1997.
|
[21]
|
P. Souplet, “The Proof of the Lane-Emden Conjecture in Four Space Dimensions,” Advances in Mathematics, Vol. 221, No. 5, 2009, pp. 1409-1427.
doi:10.1016/j.aim.2009.02.014
|
[22]
|
M. del Pino, etc., “Varia-tional Reduction for Ginzburg-Landau Vortices,” Journal of Functional Analysis, Vol. 239, No. 2, 2006, pp. 497-541.
doi:10.1016/j.jfa.2006.07.006
|
[23]
|
P. Polacik, P. Souplet and P. Quittner, “Singularity and Decay Estimates in Superlinear Problems via Liouville-Type Theorems, Part 1: Elliptic Equa-tions and Systems,” Duke Mathematical Journal, Vol. 139, No. 3, 2007, pp. 555-579. doi:10.1215/S0012-7094-07-13935-8
|
[24]
|
J. Serrin, “Entire Solutions of Nonlinear Poisson Equations,” Proceedings of London Mathematical Society, Vol. s3-24, No. 2, 1972, pp. 343-366.
|
[25]
|
Y. L. Xin, “Geometry of Harmonic Maps. Se-ries: Progress in Nonlinear Differential Equations and their Applications,” Birkhauser Boston, Inc., Boston, Vol. 23, 1996, pp. 241.
|