Positive solutions for generalized quasilinear Schrödinger equations with asymptotically linear nonlinearities

References

• Chen JH, Tang XH, Cheng BT. Non-Nehari manifold method for a class of generalized quasilinear Schrödinger equations. Appl Math Lett. 2017;74:20–26. doi: 10.1016/j.aml.2017.04.032
   Web of Science ®Google Scholar
• Deng YB, Peng SJ, Yan SS. Positive soliton solutions for generalized quasilinear Schrödinger equations with critical growth. J Differ Equ. 2015;258:115–147. doi: 10.1016/j.jde.2014.09.006
   Web of Science ®Google Scholar
• Deng YB, Peng SJ, Wang JX. Nodal soliton solutions for generalized quasilinear Schrödinger equations. J Math Phys. 2013;54:011504. doi: 10.1063/1.4774153
   Web of Science ®Google Scholar
• Li QQ, Wu X. Multiple solutions for generalized quasilinear Schrödinger equations. Math Meth Appl Sci. 2017;40:1359–1366. doi: 10.1002/mma.4050
   Web of Science ®Google Scholar
• Shen YT, Wang YJ. Soliton solutions for generalized quasilinear Schrödinger equations. Nonlinear Anal. 2013;80:194–201. doi: 10.1016/j.na.2012.10.005
   Web of Science ®Google Scholar
• Shi HX, Chen HB. Existence and multiplicity of solutions for a class of generalized quasilinear Schrödinger equations. J Math Anal Appl. 2017;452:578–594. doi: 10.1016/j.jmaa.2017.03.020
   Web of Science ®Google Scholar
• Shi HX, Chen HB. Positive solutions for generalized quasilinear Schrödinger equations with potential vanishing at infinity. Appl Math Lett. 2016;61:137–142. doi: 10.1016/j.aml.2016.06.004
   Web of Science ®Google Scholar
• Wang YJ. Solitary solutions for a class of Schrödinger equations in R3. Z Angew Math Phys. 2016;67:88. doi: 10.1007/s00033-016-0679-2
   Web of Science ®Google Scholar
• Colin M, Jeanjean L. Solutions for a quasilinear Schrödinger equations: a dual approach. Nonlinear Anal. 2004;56:213–226. doi: 10.1016/j.na.2003.09.008
   Web of Science ®Google Scholar
• Shen YT, Wang YJ. Standing waves for a class of quasilinear Schrödinger equations. Complex Var Elliptic Equ. 2016;61:817–842. doi: 10.1080/17476933.2015.1119818
   Web of Science ®Google Scholar
• Severo UB, Gloss E, da Silva ED. On a class of quasilinear Schrödinger equations with superlinear or asymptotically linear terms. J Differ Equ. 2017;263:3550–3580. doi: 10.1016/j.jde.2017.04.040
   Web of Science ®Google Scholar
• Li SH, Li JY, Chen Y. On concentration of positive ground states for the asymptotically linear fractional Schrödinger equation. J Math Phys. 2018;59:021509.
   Web of Science ®Google Scholar
• Brüll L, Lange H. Solitary waves for quasilinear Schrödinger equations. Expo Math. 1986;4:278–288.
   Google Scholar
• Laedke EW, Spatschek KH, Stenflo L. Evolution theorem for a class of perturbed envelope soliton solutions. J Math Phys. 1983;24:2764. doi: 10.1063/1.525675
   Web of Science ®Google Scholar
• Wang YJ, Li Q. Existence and asymptotic profiles of positive solutions of quasilinear Schrödinger equations in R3. J Math Phys. 2017;58:111502.
   Web of Science ®Google Scholar
• Brizhik L, Eremko A, Piette B, et al. Static solutions of a D-dimensional modified nonlinear Schrödinger equation. Nonlinearity. 2003;16:1481–1497. doi: 10.1088/0951-7715/16/4/317
   Web of Science ®Google Scholar
• Brizhik L, Eremko A, Piette B, et al. Electron self-trapping in a discrete two-dimensional lattice. Phys D. 2001;159:71–90. doi: 10.1016/S0167-2789(01)00332-3
   Web of Science ®Google Scholar
• Hartmann H, Zakrzewski WJ. Electrons on hexagonal lattices and applications to nanotubes. Phys Rev B. 2003;68:184–302. doi: 10.1103/PhysRevB.68.184302
   Web of Science ®Google Scholar
• Kurihura S. Large-amplitude quasi-solitons in superfluid films. J Phys Soc Japan. 1981;50:3262–3267. doi: 10.1143/JPSJ.50.3262
   Google Scholar
• Li QQ, Wu X. Existence, multiplicity, and concentration of solutions for generalized quasilinear Schödinger equations with critical growth. J Math Phys. 2017;58:041501.
   Web of Science ®Google Scholar
• Cheng YK, Yao YX. Soliton solutions to a class of relativistic nonlinear Schrödinger equations. Appl Math Comp. 2015;260:342–350. doi: 10.1016/j.amc.2015.03.055
   Web of Science ®Google Scholar
• Shen YT, Wang YJ. Standing waves for a relativistic quasilinear asymptotically Schrödinger equation. Appl Anal. 2016;95:2553–2564. doi: 10.1080/00036811.2015.1100296
   Web of Science ®Google Scholar
• Shen YT, Wang YJ. A class of generalized quasilinear Schrödinger equations. Commun Pure Appl Anal. 2016;3:853–870.
   Google Scholar
• Severo UB, deCarvalho GM. Quasilinear Schrödinger equations with a positive parameter and involving unbounded or decaying potentials, Appl. Anal. 2019: DOI: 10.1080/00036811.2019.1599106.
   Google Scholar
• Brezis H. Analyse fonctionnelle. Masson; 1987.
   Google Scholar
• Jeanjean L, Tanaka K. A Positive solution for an asymptotically linear elliptic problem on RN autonomous at infinity. ESAIM Control Optim Cal Var. 2002;7:597–614. doi: 10.1051/cocv:2002068
   Web of Science ®Google Scholar
• Willem M. Minimax theorems. Boston (MA): Birkhäuser Boston; 1996.
   Google Scholar
• Lions PL. The concentration-compactness principle in the calculus of variation. The locally compact case, part I and II. Ann Inst H Poincaré Anal Non Linéaire. 1984;1:109–145, 223–283. doi: 10.1016/S0294-1449(16)30428-0
   Web of Science ®Google Scholar