Multiple soliton solutions for a quasilinear Schrödinger equation

Jiayin Liu () and Duchao Liu ()
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Jiayin Liu: Beifang University of Nationalities
Duchao Liu: Lanzhou University

Indian Journal of Pure and Applied Mathematics, 2017, vol. 48, issue 1, 75-90

Abstract: 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.

Keywords: Quasilinear Schrödinger equation; soliton solution; Morse theory; symmetry mountain pass theorem; truncation arguments (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s13226-016-0195-2

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