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Global multiplicity of solutions to a defocusing quasilinear Schrödinger equation with the singular term

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Abstract

We consider a class of modified quasilinear Schrödinger equations

$$ - \Delta u + {k \over 2}u\Delta {u^2} = \lambda a\left(x \right){u^{- \alpha}} + b\left(x \right){u^\beta}\,\,\,{\rm{in}}\,\,\Omega $$

with u(x) = 0 on ∂Ω, where Ω ⊂ ℝN is a bounded domain with a regular boundary, N ≽ 3, a and b are bounded mensurable functions, 0 < α < 1 < β < 2* − 1 and k, λ ≽ 0 are two parameters. We establish the global existence and multiplicity results of positive solutions in \(H_0^1\left(\Omega \right) \cap {L^\infty}\left(\Omega \right)\) for appropriate classes of parameters k and λ and coefficients a(x) and b(x).

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Acknowledgements

The second author was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq/Brazil) (Grant No. 311562/2020-5). The third author was supported by National Natural Science Foundation of China (Grant Nos. 11971436 and 12011530199) and Natural Science Foundation of Zhejiang (Grant Nos. LZ22A010001 and LD19A010001). The fourth author was supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES/Brazil) (Grant No. 2788/2015-02).

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Siyu Chen & Minbo Yang

  2. Departamento de Matemática, Universidade de Brasília, Brasília, 70910-900, Brazil

    Carlos Alberto Santos & Jiazheng Zhou

Authors
  1. Siyu Chen
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  2. Carlos Alberto Santos
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  3. Minbo Yang
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  4. Jiazheng Zhou
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Correspondence to Siyu Chen.

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Chen, S., Santos, C.A., Yang, M. et al. Global multiplicity of solutions to a defocusing quasilinear Schrödinger equation with the singular term. Sci. China Math. 66, 1789–1812 (2023). https://doi.org/10.1007/s11425-022-2002-y

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