Global bifurcation of double phase problems

Abstract

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