Via the global bifurcation theorem due to Rabinowitz, the paper shows bifurcation properties of the solutions of the following nonlinear Dirichlet problem, involving a double phase operator, that is ( −Δap u − νΔmu = λa(x)|u|m−2u + f(x, u) in Ω, u = 0 on ∂Ω, where 1 < m < p < N, p/m < 1 + 1/N and λ, ν ∈ R.
The first aim of this paper is to discuss some of the contents of Hutson et al. [15] versus the contents of a well known paper of Y. Lou, [20], as many experts are attributing, incorrectly, to Lou [20] some of the pioneering findings of Hutson et al. [15], published 11 years before. The second aim is contextualize the most pioneering results versus the most recent ones by the team of the author. Finally, some new multiplicity and uniqueness results are given for a symmetric diffusive competition model.
