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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.
Zeng et al. (Thu,) studied this question.