Convergence analysis for double phase obstacle problems with multivalued convection term

Abstract In the present paper, we introduce a family of the approximating problems corresponding to an elliptic obstacle problem with a double phase phenomena and a multivalued reaction convection term. Denoting by 𝓢 the solution set of the obstacle problem and by 𝓢 n the solution sets of approximating problems, we prove the following convergence relation ∅ ≠ w - lim sup n → ∞ S n = s - lim sup n → ∞ S n ⊂ S, array w-₍ Sₙ=s-₍ Sₙ S, array where w -lim sup n →∞ 𝓢 n and s -lim sup n →∞ 𝓢 n denote the weak and the strong Kuratowski upper limit of 𝓢 n, respectively.