Abstract
We study the existence and multiplicity of nonnegative solutions, as well as the behavior of corresponding parameter-dependent branches, to the equation −Δu=(1−u)um−λun in a bounded domain Ω⊂RN endowed with the zero Dirichlet boundary data, where 0<m≤1 and n>0. When λ>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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