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This article is cited in 3 scientific papers (total in 3 papers)
The asymptotic behaviour of the sequence of solutions for a family of equations involving $p(\cdot)$-Laplace operators
Maria Fărcăşeanua, Mihai Mihăilescuba a Research group of the project PN-III-P4-ID-PCE-2016-0035, “Simion Stoilow” Institute of Mathematics of the Romanian Academy, 010702 Bucharest, Romania
b Department of Mathematics, University of Craiova, 200585 Craiova, Romania
Abstract:
Let $\Omega\subset\mathbb{R}^N$ be a bounded domain with smooth boundary and let $p\colon \overline\Omega\rightarrow(1,\infty)$ be a continuous function. In this paper, we establish the existence of a positive real number $\lambda^\star$ such that for each $\lambda\in(0,\lambda^\star)$ and each integer number $n>N$ the equation $-\mathrm{div}(|\nabla u(x)|^{np(x)-2}\nabla u(x))=\lambda e^{u(x)}$ when $x\in\Omega$ subject to the homogenous Dirichlet boundary condition has a nonnegative solution, say $u_n$. Next, we prove the uniform convergence of the sequence $\{u_n\}$, as $n\rightarrow\infty$, to the distance function to the boundary of the domain $\Omega$.
Key words and phrases:
variable exponent spaces, asymptotic behaviour, Ekeland's variational principle, distance function to the boundary, viscosity solution.
Citation:
Maria Fărcăşeanu, Mihai Mihăilescu, “The asymptotic behaviour of the sequence of solutions for a family of equations involving $p(\cdot)$-Laplace operators”, Mosc. Math. J., 20:3 (2020), 495–509
Linking options:
https://www.mathnet.ru/eng/mmj775 https://www.mathnet.ru/eng/mmj/v20/i3/p495
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Abstract page: | 138 | References: | 19 |
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