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arXiv · 2003.08995

Existence and multiplicity results for a class of semilinear elliptic equations

Vladimir Bobkov·Pavel Drabek·Jesus Hernandez
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Abstract

We study the existence and multiplicity of nonnegative solutions, as well as the behaviour of corresponding parameter-dependent branches, to the equation $-\Delta u = (1-u) u^m - \lambda u^n$ in a bounded domain $\Omega \subset \mathbb{R}^N$ endowed with the zero Dirichlet boundary data, where $0 0$. When $\lambda > 0$, the obtained solutions can be seen as steady states of the corresponding reaction-diffusion equation describing a model of isothermal autocatalytic chemical reaction with termination. In addition to the main new results, we formulate a few relevant conjectures.

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Vladimir Bobkov, Pavel Drabek, Jesus Hernandez. 2020-03-19. Existence and multiplicity results for a class of semilinear elliptic equations. https://doi.org/10.1016/j.na.2020.112017

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