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Existence of a Weak Solution for a Class of Nonlinear Elliptic Equations on the Sierpiński Gasket

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Ukrainian Mathematical Journal Aims and scope

We study the existence of a weak (strong) solution of a nonlinear elliptic problem

\(\begin{array}{c}-\Delta u-\lambda u{g}_{1}+h\left(u\right){g}_{2}=f\mathrm{ in }V/{V}_{0},\\ u=0\mathrm{ on }{V}_{0},\end{array}\)

where V is a Sierpiński gasket in ℝN−1, N ≥ 2, V0 is its boundary (consisting of N its corners), and λ is a real parameter. Here, f, g1, g2: V → ℝ and h : ℝ → ℝ are functions satisfying suitable hypotheses.

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Authors and Affiliations

  1. National Institute of Technology Rourkela, Odisha, India

    A. K. Badajena & R. Kar

Authors
  1. A. K. Badajena
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  2. R. Kar
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Correspondence to R. Kar.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 10, pp. 1317–1327, October, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i10.6248.

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Badajena, A.K., Kar, R. Existence of a Weak Solution for a Class of Nonlinear Elliptic Equations on the Sierpiński Gasket. Ukr Math J 74, 1500–1512 (2023). https://doi.org/10.1007/s11253-023-02151-4

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  • DOI: https://doi.org/10.1007/s11253-023-02151-4

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