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Multiple soliton solutions for a quasilinear Schrödinger equation

Author

Listed:
  • Jiayin Liu

    (Beifang University of Nationalities)

  • Duchao Liu

    (Lanzhou University)

Abstract

Using Morse theory, truncation arguments and an abstract critical point theorem, we obtain the existence of at least three or infinitely many nontrivial solutions for the following quasilinear Schrödinger equation in a bounded smooth domain (0.1) $$\left\{ {\begin{array}{*{20}{c}} { - {\Delta _p}u - \frac{p}{{{2^{p - 1}}}}u{\Delta _p}\left( {{u^2}} \right) = f\left( {x,u} \right)\;in\;\Omega } \\ {u = 0\;on\;\partial \Omega .} \end{array}} \right.$$ { − Δ p u − p 2 p − 1 u Δ p ( u 2 ) = f ( x , u ) i n Ω u = 0 o n ∂ Ω . Our main results can be viewed as a partial extension of the results of Zhang et al. in [28] and Zhou and Wu in [29] concerning the the existence of solutions to (0.1) in the case of p = 2 and a recent result of Liu and Zhao in [21] two solutions are obtained for problem 0.1.

Suggested Citation

  • Jiayin Liu & Duchao Liu, 2017. "Multiple soliton solutions for a quasilinear Schrödinger equation," Indian Journal of Pure and Applied Mathematics, Springer, vol. 48(1), pages 75-90, March.
    • Handle: RePEc:spr:indpam:v:48:y:2017:i:1:d:10.1007_s13226-016-0195-2
    DOI: 10.1007/s13226-016-0195-2
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