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Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 11
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Articles

Existence of solutions for a perturbed p-Laplacian system with critical exponent in

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Pages 1885-1905 | Received 06 Feb 2016, Accepted 02 Jun 2016, Published online: 25 Jun 2016

References

  • Kurihara S. Large-amplitude quasi-solitons in superfluid films. J. Phys. Soc. Japan. 1981;50:3262–3267.
  • Brandi H, Manus C, Mainfray G, Lehner T, Bonnaud G. Relativistic and ponderomotive self-focusing of a laser beam in a radially inhomogeneous plasma. Phys. Fluids B. 1993;5:3539–3550.
  • Chen XL, Sudan RN. Necessary and sufficient conditions for self-focusing of short ultraintense laser pulse in underdense plasma. Phys. Rev. Lett. 1993;70:2082–2085.
  • De Bouard A, Hayashi N, Saut J. Global existence of small solutions to a relativistic nonlinear Schrödinger equation. Comm. Math. Phys. 1997;189:73–105.
  • Poppenberg M, Schmitt K, Wang Z. On the existence of soliton solutions to quasilinear Schrödinger equations. Calc. Var. Partial Differ. Equ. 2002;14:329–344.
  • Bass FG, Nasanov NN. Nonlinear electromagnetic-spin waves. Phys. Rep. 1990;189:165–223.
  • Brüll L, Lange H. Solitary waves for quasilinear Schrödinger equations. Exposition. Math. 1986;4:279–288.
  • Kosevich AM, Ivanov BA, Kovalev AS. Magnetic solutions. Phys. Rep. 1990;194:117–238.
  • Lin X, Tang XH. Semiclassical solutions of perturbed p-Laplacian equations with critical nonlinearity. J. Math. Anal. Appl. 2014;413:438–449.
  • Wang C, Wang J. Solutions of perturbed p-Laplacian equations with critical nonlinearity. J. Math. Phys. 2013;54:013702.
  • Ding Y, Lin F. Solutions of perturbed Schrödinger equations with critical nonlinearity. Calc. Var. 2007;30:231–249.
  • Ambrosetti A, Badiale M, Cingolani S. Semiclassical states of nonlinear Schrödinger equations. Arch. Ration. Mech. Anal. 1997;140:285–300.
  • Floer A, Weinstein A. Nonspreading wave packets for the cubic Schrodinger equation with a bounded potential. J. Funct. Anal. 1986;69:397–408.
  • Grossi M. Some results on a class of nonlinear Schrödinger equations. Math. Z. 2000;235:687–705.
  • Jeanjean L, Tanaka K. Singularly perturbed elliptic problems with superlinear or asymptotically linear nonlinearities. Calc. Var. Partial Differ. Equ. 2004;21:287–318.
  • Pistoia A. Multi-peak solutions for a class of nonlinear Schrödinger equations. Nonlinear Differ. Equ. Appl. 2002;9:69–91.
  • Wang X. On concentration of positive bound states of nonlinear Schrodinger equations. Commun. Math. Phys. 1993;153:229–244.
  • Severo U, da Silva E. On the existence of standing wave solutions for a class of quasilinear Schrödinger systems. J. Math. Anal. Appl. 2014;412:763–775.
  • José FL. Aires, Marco A.S. Souto, Existence of solutions for a quasilinear Schrödinger equation with vanishing potentials. J. Math. Anal. Appl. 2014;416:924–946.
  • Wang Y, Zhang Y, Shen Y. Multiple solutions for quasilinear Schrödinger equations involving critical exponent. Applied Mathematics and Computation. 2010;216:849–856.
  • Liu J, Wang Y, Wang Z. Soliton solutions for quasilinear Schrödinger equations II. J. Differ. Equ. 2003;187:473–493.
  • Liu J, Wang Z. Symmetric solutions to a modified nonlinear Schrödinger equation. Nonlinearity. 2008;21:121–133.
  • Liu J. Z. Wang, Soliton solutions for quasilinear Schrödinger equations. I. Proc. Am. Math. Soc. 2003;131:441–448.
  • Liu J, Wang Y, Wang Z. Solutions for quasilinear Schrödinger equations via the Nehari method. Commun. Partial Differ. Equ. 2004;29:879–901.
  • Wang Y, Yao Y. Standing waves for quasilinear Schrödinger equations. J. Math. Anal. Appl. 2013;400:305–310.
  • Deng Y, Peng S, Yan S. Critical exponents and solitary wave solutions for generalized quasilinear Schrödinger equations. J. Differ. Equ. 2016;260:1228–1262.
  • Wu X. Multiple solutions for quasilinear Schrödinger equations with a parameter. J. Differ. Equ. 2014;256:2619–2632.
  • do Ó JM, Miyagaki O, Soares S. Soliton solutions for quasilinear Schrödinger equations: the critical exponential case. Nonlinear Anal. 2007;67:3357–3372.
  • Yang M, Ding Y. Existence of semiclassical states for a quasilinear Schr\"{o}dinger equation with critical exponent in RN. Anal. Matematica. 2013;192:783–804.
  • Alves MJ, Carriáo PC, Miyagaki OH. Non-autonomous perturbations for a class of quasilinear elliptic equations on R. J. Math. Anal. Appl. 2008;344:186–203.
  • Severo U. Existence of weak solutions for quasilinear elliptic equations involving the p-Laplacian. Electronic J. Differ. Equ. 2008;56:1–16.
  • Alves CO, Figueiredo GM. Multiple solutions for a quasilinear Schrödinger equation on RN. Acta. Appl. Math. 2015;136:91–117.
  • Liu D. Soliton solutions for a quasilinear Schrödinger equation. Electronic J. Differ. Equ. 2013;267:1–13.
  • Wang J, Wang L, Zhang D. Solutions of semiclassical states for perturbed p-Laplacian equation with critical exponent. Boundary Value Prob. 2014;2014:243.
  • Chen C, Song H. Soliton solutions for quasilinear Schrödinger equation with critical exponential growth in RN. Applications of Mathematics. 2016;61:317–337.
  • Wang Y, Yang J, Zhang Y. Quasilinear elliptic equations involving the N-Laplacian with critical exponential growth in RN. Nonlinear Anal. 2009;71:6157–6169.
  • Song H, Chen C, Yan Q. Infinitely many solutions for quasilinear Schrödinger equation with critical exponential growth in RN. J. Math. Anal. Appl. 2016;439:575–593.
  • Colin M, Jeanjean L. Solutions for a quasilinear Schrödinger equation: a dual approach. Nonlinear Anal. 2004;56:213–226.
  • do Ó JM, Miyagaki O, Soares S. Soliton solutions for quasilinear Schrödinger equations with critical growth. J. Differ. Equ. 2010;248:722–744.
  • Brezis H, Lieb E. A relation between pointwise convergence of functions and convergence of functionals. Proc. Am. Math. Soc. 1983;88:437–477.
  • Han P. The effect of the domain topology on the number of positive solutions of elliptic systems involving critical Sobolev exponents. Houston J. Math. 2006;32:1241–1257.

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