The main purpose of this article is to improve classical weighted Hardy type inequalities by adding infinitely many sharp new missing terms. The key of proof is to construct a family of positive solutions for ordinary differential equations involving slowly increasing functions in their coefficients.
A family of slowly increasing functions has been introduced in . The main purpose of this article is to study further properties of slowly increasing functions. More specifically, we concentrate on constructing a family of differential equations involving slowly increasing functions in their coefficients.
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