We consider boundary value problems in a half-space for a class of quasielliptic systems with nonzero boundary functions.We assume that the boundary value problems satisfy the Lopatinskiĭ condition. Necessary conditions are given for their unique solvability in Sobolev spaces. In a particular case, these conditions coincide with sufficient conditions.

中文翻译：

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一类拟椭圆系统边值问题可解的必要条件。

我们考虑一类具有非零边界函数的拟椭圆系统的半空间中的边值问题，并假设边值问题满足Lopatinskiĭ条件。给出了它们在Sobolev空间中独特的可溶性的必要条件。在特定情况下，这些条件与足够的条件一致。