Quasilinear elliptic equations with critical growth via perturbation method
Tài liệu tham khảo
Ambrosetti, 2003, Positive solutions to a class of quasilinear elliptic equations on R, Discrete Contin. Dyn. Syst., 9, 55, 10.3934/dcds.2003.9.55
Arcoya, 1999, Some remarks on critical point theory for nondifferentiable functionals, NoDEA Nonlinear Differential Equations Appl., 6, 79, 10.1007/s000300050066
Alves, 2009, Multiplicity of positive solutions for a class of quasilinear problems, Adv. Differential Equations, 14, 911, 10.57262/ade/1355863334
Brezis, 1983, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math., 36, 437, 10.1002/cpa.3160360405
Brihaye, 2006, Solitons on nanotubes and fullerenes as solutions of a modified nonlinear Schrödinger equation, 135
Brizhik, 2003, Static solutions of a D-dimensional modified nonlinear Schrödinger equation, Nonlinearity, 16, 1481, 10.1088/0951-7715/16/4/317
Brüll, 1986, Solitary waves for quasilinear Schrödinger equations, Expo. Math., 4, 278
Canino, 1995, Nonsmooth critical point theory and quasilinear elliptic equations, vol. 472, 1
Colin, 2002, On the local well-posedness of quasilinear Schrödinger equations in arbitrary space dimension, Comm. Partial Differential Equations, 27, 325, 10.1081/PDE-120002789
Colin, 2004, Solutions for a quasilinear Schrödinger equation: A dual approach, Nonlinear Anal., 56, 213, 10.1016/j.na.2003.09.008
Colin, 2010, Stability and instability results for standing waves of quasilinear Schrödinger equations, Nonlinearity, 23, 1353, 10.1088/0951-7715/23/6/006
de Bouard, 1997, Global existence of small solutions to a relativistic nonlinear Schrödinger equation, Comm. Math. Phys., 189, 73, 10.1007/s002200050191
do Ó, 2010, Soliton solutions for quasilinear Schrödinger equations with critical growth, J. Differential Equations, 248, 722, 10.1016/j.jde.2009.11.030
do Ó, 2010, Solitary waves for a class of quasilinear Schrödinger equations in dimension two, Calc. Var. Partial Differential Equations, 38, 275, 10.1007/s00526-009-0286-6
Han, 2000
Hartmann, 2003, Electrons on hexagonal lattices and applications to nanotubes, Phys. Rev. B, 68, 184302, 10.1103/PhysRevB.68.184302
Hasse, 1980, A general method for the solution of nonlinear soliton and kink Schrödinger equations, Z. Phys. B, 37, 83, 10.1007/BF01325508
Kenig, 2004, The Cauchy problem for quasilinear Schrödinger equations, Invent. Math., 158, 343, 10.1007/s00222-004-0373-4
Kurihura, 1981, Large-amplitude quasi-solitons in superfluid films, J. Phys. Soc. Japan, 50, 3262, 10.1143/JPSJ.50.3262
Lange, 1999, Nash–Moser methods for the solutions of quasilinear Schrödinger equations, Comm. Partial Differential Equations, 24, 1399, 10.1080/03605309908821469
Lins, 2009, Quasilinear asymptotically periodic elliptic equations with critical growth, Nonlinear Anal., 71, 2890, 10.1016/j.na.2009.01.171
Lions, 1984, The concentration–compactness principle in the calculus of variations. The locally compact case, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1, 109, 10.1016/S0294-1449(16)30428-0
Liu, 2003, Soliton solutions for quasilinear Schrödinger equations, II, J. Differential Equations, 187, 473, 10.1016/S0022-0396(02)00064-5
Liu, 2004, Solutions for quasilinear Schrödinger equations via the Nehari method, Comm. Partial Differential Equations, 29, 879, 10.1081/PDE-120037335
Liu, 2003, Soliton solutions for quasilinear Schrödinger equations, I, Proc. Amer. Math. Soc., 131, 441, 10.1090/S0002-9939-02-06783-7
X.-Q. Liu, J.-Q. Liu, Z.-Q. Wang, Quasilinear elliptic equations via perturbation method, Proc. Amer. Math. Soc., in press, http://dx.doi.org/10.1090/S0002-9939(2012)11293-6, electronically online on May 2012.
X.-Q. Liu, J.-Q. Liu, Z.-Q. Wang, Ground states for quasilinear Schrödinger equations with critical growth, Calc. Var. Partial Differential Equations, in press, http://dx.doi.org/10.1007/s00526-012-0497-0, electronically online on January 2012.
Moameni, 2006, Existence of soliton solutions for a quasilinear Schrödinger equation involving critical growth in R, J. Differential Equations, 229, 570, 10.1016/j.jde.2006.07.001
Moameni, 2007, On a class of periodic quasilinear Schrödinger equations involving critical growth in R2, J. Math. Anal. Appl., 334, 775, 10.1016/j.jmaa.2007.01.020
Poppenberg, 2001, On the local well posedness of quasilinear Schrödinger equations in arbitrary space dimension, J. Differential Equations, 172, 83, 10.1006/jdeq.2000.3853
Poppenberg, 2002, On the existence of solutions to quasilinear Schrödinger equations, Calc. Var. Partial Differential Equations, 14, 329, 10.1007/s005260100105
Pucci, 1986, A general variational identity, Indiana Univ. Math. J., 35, 681, 10.1512/iumj.1986.35.35036
Rabinowitz, 1986, Minimax Methods in Critical Point Theory with Applications to Differential Equations, vol. 65
Silva, 2010, Quasilinear asymptotically periodic Schrödinger equations with critical growth, Calc. Var. Partial Differential Equations, 39, 1, 10.1007/s00526-009-0299-1
Silva, 2010, Quasilinear asymptotically periodic Schrödinger equations with subcritical growth, Nonlinear Anal., 72, 2935, 10.1016/j.na.2009.11.037