A version of biting lemma for unbounded sequences in L[sub E][sup 1] with applications

Abstract

The aim of the present work is to introduce the notion of finite tightness and then to obtain some results of compactness in the lack of L 1 -boundedness. We use these results in order to obtain information about the limit of the solutions for a sequence of one dimensional heat equations.

Convergence results for solutions of a first-order differential equation

“…In a first variant, we introduced Jordan finite-tight sets in the case of real functions of real variable in [6], where we presented an alternative to the paper [4] for the particular problem u (t) = f n (t), u(0) = u(1) = 0.…”