Nonexistence of solutions for quasilinear Schrödinger equation in ℝ^N

References

• Kurihura S. Large-amplitude quasi-solitons in superfluid films. J Phys Soc Japan. 1981;50:3262–3267.
   Google Scholar
• Laedke E, Spatschek K, Stenflo L. Evolution theorem for a class of perturbed envelope soliton solutions. J Math Phys. 1963;24:2764–2769.
   Google Scholar
• Bouard ADe, Hayashi N, Saut J. Global existence of small solutions to a relativistic nonlinear Schrödinger equation. Commun Math Phys. 1997;189:73–105.
   Web of Science ®Google Scholar
• Quispel GRW, Capel HW. Equation of motion for the Heisenberg spin chain. Physica A. 1982;110:41–80.
   Web of Science ®Google Scholar
• Hasse RW. A general method for the solution of nonlinear soliton and kink Schrödinger equation. Z Phys B. 1980;37:83–877.
   Google Scholar
• Makhankov VG, Fedyanin VK. Nonlinear effects in quasi-one-dimensional models of condensed matter theory. Phys Rep. 1984;104:1–86.
   Web of Science ®Google Scholar
• Liu JQ, Wang YQ, Wang ZQ. Soliton solutions to quasilinear Schrödinger equations II. J Differ Equ. 2003;187:473–493.
   Web of Science ®Google Scholar
• Liu JQ, Wang ZQ. Soliton solutions for quasilinear Schrödinger equations, I. Proc Am Math Soc. 2002;131(2):441–448.
   Web of Science ®Google Scholar
• Poppenberg M, Schmitt K, Wang ZQ. On the existence of soliton solutions to quasilinear Schrödinger equations. Calc Var Partial Differ Equ. 2002;14:329–344.
   Web of Science ®Google Scholar
• Bezerra do Ó JM, Severo U. Solitary waves for a class of quasilinear Schrödinger equations in dimension two. Calc Var Partial Differ Equ. 2010;38:275–315.
   Web of Science ®Google Scholar
• Colin M, Jeanjean L. Solutions for a quasilinear Schrödinger equations: a dual approach. Nonlinear Anal. 2004;56:213–226.
   Web of Science ®Google Scholar
• Liu JQ, Wang YQ, Wang ZQ. Solutions for quasilinear Schrödinger equations via Nehari method. Commun Partial Differ Equ. 2004;29:879–904.
   Web of Science ®Google Scholar
• Ruiz D, Siciliano G. Existence of ground states for a modified nonlinear Schrödinger equation. Nonlinearity. 2010;23:1221–1233.
   Web of Science ®Google Scholar
• Aires JFL, Souto MAS. Existence of solutions for a quasilinear Schrödinger equation with vanishing potentials. J Math Anal Appl. 2014;416:924–946.
   Web of Science ®Google Scholar
• Bezerra do Ó JM, Miyagaki OH, Soares SHM. Soliton solutions for quasilinear Schrödinger equations with critical growth. J Differ Equ. 2010;248:722–744.
   Web of Science ®Google Scholar
• Fang XD, Szulkin A. Multiple solutions for a quasilinear Schrödinger equation. J Differ Equ. 2013;254:2015–2032.
   Web of Science ®Google Scholar
• Wu X. Multiple solutions for quasilinear Schrödinger equations with a parameter. J Differ Equ. 2014;256:2619–2632.
   Web of Science ®Google Scholar
• Chen CS, Song HX, Yang HW. Liouville type theorems for stable solutions of p-Laplace equation in RN. Nonlinear Anal. 2017;160:44–52.
   Web of Science ®Google Scholar
• Chen CS, Song HX, Yang HW. Liouville-type theorems for stable solutions of singular quasilinear elliptic equations in RN. Electron J Differ Equ. 2018;81:1–11.
   Google Scholar
• Damascelli L, Farina A, Sciunzi B. Enrico Valdinoci, Liouville results for m-Laplace equations of Lane–Emden–Fowler type. Ann Inst H. Poincaré Anal Non Linéaire. 2009;26:1099–1119.
   Web of Science ®Google Scholar
• Kuzin I, Pohozaev S. Entire solutions of semilinear elliptic equations. Basel:Birkhäuser; 1997. (Progress in nonlinear differential equations and their applications; vol. 33).
   Google Scholar
• Lu CN, Fu C, Yang HW. Time-fractional generalized Boussinesq equation for Rossby solitary waves with dissipation effect in stratified fluid and conservation laws as well as exact solutions. Appl Math Comput. 2018;327:104–116.
   Web of Science ®Google Scholar
• Ghergu M, Rădulescu V. Singular elliptic problems with lack of compactness. Ann Matematica. 2006;185:63–79.
   Web of Science ®Google Scholar
• Li YH, Li FY, Shi JP. Existence of positive solutions to Kirchhoff type problems with zero mass. J Math Anal Appl. 2014;410:361–374.
   Web of Science ®Google Scholar
• Evans LC. Partial differential equations.Rhode Island: American Mathematical Society; 1998. (Graduate studies in mathematics; vol. 19).
   Google Scholar
• Severo U. Existence of weak solutions for quasilinear elliptic equations involving the p-Laplacian. Elec J Differ Equ. 2008;56:1–16.
   Google Scholar
• Serrin J. Local behavior of solutions of quasi-linear equations. Acta Math. 1964;111:247–302.
   Web of Science ®Google Scholar
• D'Ambrosio L, Mitidieri E. Quasilinear elliptic equations with critical potentials. Adv Nonlinear Anal. 2017;6(2):147–164.
   Web of Science ®Google Scholar
• Le P. Liouville theorems for stable solutions of p-Laplace equations with convex nonlinearities. J Math Anal Appl. 2016;443:431–444.
   Web of Science ®Google Scholar