Existence of a weak solution for a class of nonlinear elliptic equations on the Sierpiński gasket

  • A. K. Badajena Nat. Inst. Technology Rourkela, Odisha, India
  • R. Kar Nat. Inst. Technology Rourkela, Odisha, India
Keywords: Sierpinski gasket, Nonlinear elliptic equations, Fractal domains, Demicontinu- ous operators.

Abstract

UDC 517.9

We study the existence of a weak (strong) solution of the nonlinear elliptic problem\begin{gather*} -\Delta u- \lambda ug_1 +h(u)g_2=f \quad\text{in}\quad V\setminus V_0,\\u=0 \quad\text{on}\quad V_0,\end{gather*} where $V$ is a Sierpi\'nski gasket in $\mathbb{R}^{N-1},$ $N\geq 2,$ $V_0$ is its boundary (consisting of $N$ its corners), and $\lambda$ is a real parameter. Here, $f,g_1,g_2\colon V\to\mathbb{R}$ and $h\colon \mathbb{R}\to\mathbb{R}$ are functions satisfying suitable hypotheses.

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Published
27.11.2022
How to Cite
BadajenaA. K., and KarR. “Existence of a Weak Solution for a Class of Nonlinear Elliptic Equations on the Sierpiński Gasket”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 10, Nov. 2022, pp. 1317 -27, doi:10.37863/umzh.v74i10.6248.
Section
Research articles