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 𝓢n the solution sets of approximating problems, we prove the following convergence relation ∅≠w-lim supn→∞Sn=s-lim supn→∞Sn⊂S, $$\begin{array}{} \displaystyle \emptyset\neq w\text{-}\limsup\limits_{n\to\infty}{\mathcal S}_n=s\text{-}\limsup\limits_{n\to\infty}{\mathcal S}_n\subset \mathcal S, \end{array}$$ where w-lim supn→∞ 𝓢n and s-lim supn→∞ 𝓢n denote the weak and the strong Kuratowski upper limit of 𝓢n, respectively.

中文翻译：

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多值对流项双相障碍问题的收敛性分析

摘要 在本文中，我们介绍了与具有双相现象和多值反应对流项的椭圆障碍问题相对应的一系列近似问题。用𝓢表示障碍问题的解集，用𝓢n表示逼近问题的解集，我们证明以下收敛关系 ∅≠w-lim supn→∞Sn=s-lim supn→∞Sn⊂S, $$\begin {array}{} \displaystyle \emptyset\neq w\text{-}\limsup\limits_{n\to\infty}{\mathcal S}_n=s\text{-}\limsup\limits_{n\to\ infty}{\mathcal S}_n\subset \mathcal S, \end{array}$$ 其中 w-lim supn→∞ 𝓢n 和 s-lim supn→∞ 𝓢n 分别表示𝓢n 的弱和强 Kuratowski 上限.