先给出这些问题的提法，然后使用列紧性原理和极值原理证明了上述二阶椭圆型方程边值解的存在性和唯一性。

Fristly the boundary value problems for the equations is formulated, and then by using the compactness principle, the existence of solutions for the above problems is proved.

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线性算子为紧线性算子必须且仅须它可由一列有限秩连续齐性算子一致逼近。

It follows that a linear operator is a compact linear operator iff it an be approximated uniformly by a sequence of finite rank continuous homogeneous operators.

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运用改进的集中列紧原理证明了在某些指数条件下非奇对称的临界非线性项仍能保证无穷多弱解的存在性。

The problem involves non-odd symmetric critical nonlinearity. Existence of infinitely many solutions of this problem is obtained with improved Compactness- Concentration principle.

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