Asymptotical behavior of ground state solutions for critical quasilinear Schrödinger equation

Yongpeng CHEN , Yuxia GUO , Zhongwei TANG

Front. Math. China ›› 2020, Vol. 15 ›› Issue (1) : 21 -46.

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Front. Math. China ›› 2020, Vol. 15 ›› Issue (1) : 21 -46. DOI: 10.1007/s11464-020-0825-1
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Asymptotical behavior of ground state solutions for critical quasilinear Schrödinger equation

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Abstract

This paper is concerned with the existence and asymptotical behavior of positive ground state solutions for a class of critical quasilinear Schrodinger equation. By using a change of variables and variational argument, we prove the existence of positive ground state solution and discuss their asymptotical behavior.

Keywords

Quasilinear Schrödinger equation / critical exponent / ground state solution / asymptotical behavior

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Yongpeng CHEN, Yuxia GUO, Zhongwei TANG. Asymptotical behavior of ground state solutions for critical quasilinear Schrödinger equation. Front. Math. China, 2020, 15(1): 21-46 DOI:10.1007/s11464-020-0825-1

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References

[1]

Aires J, Souto M. Existence of solutions for a quasilinear Schrödinger equation with vanishing potentials. J Math Anal Appl, 2014, 416: 924–946

[2]

Alves C, Barros L. Existence and multiplicity of solutions for a class of elliptic problem with critical growth. Monatsh Math, 2018, 187: 195–215

[3]

Bartsch T, Wang Z. Multiple positive solutions for a nonlinear Schrödinger equation. Z Angew Math Phys, 2000, 51: 366–384

[4]

Colin M, Jeanjean L. Solutions for a quasilinear Schrödinger equation: a dual approach. Nonlinear Anal, 2004, 56: 213–226

[5]

Deng Y, Peng S, Yan S. Positive soliton solutions for generalized quasilinear Schrödinger equations with critical growth. J Differential Equations, 2017, 37: 4213–4230

[6]

Do Ó J, Miyagaki O, Soares S. Soliton solutions for quasilinear Schrödinger equations with critical growth. J Differential Equations, 2010, 248: 722–744

[7]

Do Ó J, Severo U. Quasilinear Schrödinger equation involving concave and convex non-linearities. Commun Pure Appl Anal, 2009, 8: 621–644

[8]

Guo Y, Tang Z. Ground state solutions for the quasilinear Schrödinger equations. Nonlinear Anal, 2012, 75: 3235–3248

[9]

Guo Y, Tang Z. Multi-bump bound state solutions for the quasilinear Schrödinger equations with critical frequency. Pacific J Math, 2014, 270: 49–77

[10]

He X, Qian A, Zou W. Existence and concentration of positive solutions for quasilinear Schrödinger equations with critical growth. Nonlinearity, 2013, 26: 3137–3168

[11]

He Y, Li G. Concentrating soliton solutions for quasilinear Schrödinger equations involving critical Sobolev exponents. Discrete Contin Dyn Syst, 2016, 36: 731–762

[12]

Li Z, Zhang Y. Solutions for a class of quasilinear Schrödinger equations with critical Sobolev exponents. J Math Phys, 2017, 58: 1–15

[13]

Liang S, Zhang J. Existence of multi-bump solutions for a class of quasilinear Schrödinger equations in ℝN involving critical growth. Milan J Math, 2015, 83: 55–90

[14]

Liu J, Wang Y, Wang Z. Soliton solutions for quasilinear Schrödinger equation, II. J Differential Equations, 2003, 187: 473–493

[15]

Liu J, Wang Y, Wang Z. Solutions for quasilinear Schrödinger equation via Nehari method. Comm Partial Differential Equations, 2004, 29: 879–901

[16]

Liu S, Zhou J. Standing waves for quasilinear Schrödinger equations with indefinite potentials. J Differential Equations, 2018, 265: 3970–3987

[17]

Liu X, Liu J, Wang Z. Quasilinear elliptic equations via perturbation method. Proc Amer Math Soc, 2013, 141: 253–263

[18]

Shen Y, Wang Y. Soliton solutions for generalized quasilinear Schrödinger equations. Nonlinear Analysis TMA, 2013, 80: 194–201

[19]

Silva E, Vieira G. Quasilinear asymptotically periodic Schrödinger equations with critical growth. Calc Var Partial Differential Equations, 2010, 39: 1–33

[20]

Wang W, Yang X, Zhao F. Existence and concentration of ground state to a quasilinear problem with competing potentials. Nonlinear Anal, 2014, 102: 120–132

[21]

Wang Y, Zhang Y, Shen Y. Multiple solutions for quasilinear Schrödinger equations involving critical exponent. Appl Math Comput, 2010, 216: 849–856

[22]

Wang Y, Zou W. Bound states to critical quasilinear Schrödinger equations. NoDEA Nonlinear Differential Equations Appl, 2012, 19: 19–47

[23]

Willem M. Minimax Theorem. Boston: Birkhäuser, 1996

[24]

Wu K. Positive solutions of quasilinear Schrödinger equations critical growth. Appl Math Lett, 2015, 45: 52–57

[25]

Xu L, Chen H. Ground state solutions for quasilinear Schrödinger equation via Pohozaev manifold in Orlicz space. J Differential Equations, 2018, 265: 4417–4441

[26]

Zeng X, Zhang Y, Zhou H. Positive solutions for a quasilinear Schrödinger equation involving Hardy potential and critical exponent. Commun Contemp Math, 2014, 16: 1–32

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