[1] Alves C O, Wang Y, Shen Y. Soliton solutions for a class of quasilinear Schrödinger equations with a parameter. J Differential Equations, 2015, 259:318-343 [2] Bartsch T, Wang Z Q. Existence and multiplicity results for some superlinear elliptic problems on RN. Comm Part Diff Eq, 1995, 20:1725-1741 [3] de Bouard A, Hayashi N, Saut J C. Global existence of small solutions to a relativistic nonlinear Schrödinger equation. Comm Math Phys, 1997, 189:73-105 [4] Brull L, Lange H. Solitary waves for quasilinear Schrödinger equations. Expo Math, 1986, 4:278-288 [5] Chen X L, Sudan R N. Necessary and sufficient conditions for self-focusing of short ultraintense laser pulse in underdense plasma. Phys Rev Lett, 1993, 70:2082-2085 [6] Colin M, Jeanjean L. Solutions for a quasilinear Schrödinger equation:a dual approach. Nonlinear Anal, 2004, 56:213-226 [7] Del Pino M, Felmer P. Local Mountain Pass for semilinear elliptic problems in unbounded domains. Calc Var Partial Differential Equations, 1996, 4:121-137 [8] Deng Y, Peng S, Yan S. Positive soliton solutions for generalized quasilinear Schrödinger equations with critical growth. J Differential Equations, 2015, 258:115-147 [9] Furtado M F, Silva E D, Silva M L. Quasilinear Schrödinger equations with asymptotically linear nonlinearities. Adv Nonlinear Stud, 2014, 14:671-686 [10] Furtado M F, Silva E D, Silva M L. Quasilinear elliptic problems under asymptotically linear conditions at infinity and at the origin. Z Angew Math Phys, 2015, 66:277-291 [11] Hasse R W. A general method for the solution of nonlinear soliton and kink Schrödinger equations. Z Phys, 1980, 37:83-87 [12] Kosevich A M, Ivanov B, Kovalev A S. Magnetic solitons. Phys Rep, 1990, 194:117-238 [13] Kurihura S. Large-amplitude quasi-solitons in superfluid films. J Phys Soc Japan, 1981, 50:3263-3267 [14] Landau L D, Lifschitz E M. Quantum Mechanics, Non-relativistic Theory. Institute of Physical Problems URSS, Academy of Sciences, 1958 [15] Li Q, Wu X. Existence, multiplicity and concentration of solutions for generalized quasilinear Schrödinger equations with critical growth. J Math Phys, 2017, 58:041501 [16] Lions P L. The concentration-compactness principle in the calculus of variations. The locally compact case. Ann Inst H Poincaré Anal Non Linéaire, 1984, 1:109-145; 223-283 [17] Litvak A G, Sergeev A M. One dimensional collapse of plasma waves. JETP Lett, 1978, 27:517-520 [18] Liu J Q, Wang Z Q. Soliton solutions for quasilinear Schrödinger equations I. Proc Amer Math Soc, 2002, 131:441-448 [19] Liu J Q. Wang Y Q, Wang Z Q. Soliton solutions for quasilinear Schrödinger equations II. J Differential Equations, 2003, 187:473-493 [20] Liu J Q, Wang Y Q, Wang Z Q. Solutions for quasilinear Schrödinger equations via the Nehari method. Comm Partial Differential Equations, 2004, 29:879-901 [21] Liu X, Liu J, Wang Z Q. Ground states for quasilinear Schrödinger equations with critical growth. Calc Var Partial Differential Equations, 2013, 46:641-669 [22] Liu S, Zhou J. Standing waves for quasilinear Schrödinger equations with indefinite potentials. Journal of Differential Equations, 2018, 265:3970-3987 [23] Makhankov V G, Fedyanin V K. Non-linear effects in quasi-one-dimensional models of condensed matter theory. Physics Reports, 1984, 104:1-86 [24] Nakamura A. Damping and modification of exciton solitary waves. J Phys Soc Jpn, 1977, 42:1824-1835 [25] do Ó J M, Severo U B. Quasilinear Schrödinger equations involving concave and convex nonlinearities. Commun Pure Appl Anal, 2009, 8:621-644 [26] do Ó J M, Miyagaki O H, Soares S H. Soliton solutions for quasilinear Schrödinger equations with critical growth. J Differential Equations, 2010, 248:722-744 [27] Poppenberg M, Schmitt K, Wang Z Q. On the existence of soliton solutions to quasilinear Schrödinger equations. Calc Var Partial Differential Equations, 2002, 14:329-344 [28] Rabinowitz P. Minimax methods in critical point theory with applications to differential equations. CBMS Reg Conf Ser Math. Vol 65. Providence RI:Amer Math Soc, 1986 [29] Rabinowitz P. On a class of nonlinear Schrödinger equations. Z Angew Math Phys, 1992, 43:270-291 [30] Schechter M, Tintarev K. Pairs of critical points produced by linking subsets with applications to semilinear elliptic problems. Bull Soc Math Belg Ser B, 1992, 44:249-261 [31] Schechter M. Linking methods in critical point theory. Boston, MA:Birkhäuser Boston, Inc, 1999 [32] Schechter M. A variation of the mountain pass lemma and applications. J London Math Soc, 1991, 44(2):491-502 [33] Silva E A B. Linking theorems and applications to semilinear elliptic problems at resonance. Nonlinear Anal, 1991, 16:455-477 [34] Silva E A B, Vieira G F. Quasilinear asymptotically periodic Schrödinger equations with subcritical growth. Nonlinear Analysis, 2010, 72:2935-2949 [35] Silva E A B, Vieira G F. Quasilinear asymptotically periodic Schrödinger equations with critical growth. Cal Var, 2010, 39:1-33 [36] Silva E D, Silva J S. Quasilinear Schrödinger equations with nonlinearities interacting with high eigenvalues. J Math Phys, 2019, 60:081504 [37] Silva E D, Silva J S. Multiplicity of solutions for critical quasilinear Schrödinger equations using a linking structure. Discrete Continuous Dynamical Systems-A, 2020, 40(9):5441-5470 [38] Souto M A S, Soares S H M. Ground state solutions for quasilinear stationary Schrödinger equations with critical growth. Commun Pure Appl Anal, 2013, 12(1):99-116 [39] Willem M. Minimax Theorems. Basel, Berlin:Birkhäuser Boston, 1996 |