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    • Soliton solutions for a quasilinear Schrödinger equation via Morse theory

      Duchao Liu Peihao Zhao

      Volume 125 Issue 3 August 2015 pp 307-321

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/125/03/0307-0321

    • Keywords

       

      Quasilinear Schrödinger equation; soliton solution; critical point; Morse theory; local linking.

    • Abstract

       

      In this paper, Morse theory is used to show the existence of nontrivial weak solutions to a class of quasilinear Schrödinger equation of the form

      $$-\Delta u - \frac{p}{2^{p-1}} u \Delta_p (u^2) = f(x, u)$$

      in a bounded smooth domain $\Omega \subset \mathbb{R}^N$ with Dirichlet boundary condition.

    • Author Affiliations

       

      Duchao Liu1 Peihao Zhao1

      1. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People’s Republic of China

    • Dates

       
      Published
      August 2015
      Manuscript received
      21 June 2013
      Manuscript revised
      15 June 2014

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