Existence and multiplicity results for a class of semilinear elliptic equations

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 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