Sufficient conditions for the controllability of nonlinear neutral Volterra integrodifferential systems with implicit derivative are established. The results are a generalisation of the previous results, through the notions of condensing map and measure of noncompactness of a set.

Two homogeneous measures of noncompactness β and γ on an infinite dimensional Banach space X are called “equivalent” if there exist positive constants b and c such that bβ(S) ≤ γ (S) ≤ cβ(S) for all bounded sets S ⊂ X . If such constants do not exist, the measures of noncompactness are “inequivalent.”Weask a foundational questionwhich apparently has not previously been considered: For what infi...

We compute the precise value of measure noncompactness Sobolev embeddings $W_0^{1,p}(D)\hookrightarrow L^p(D)$, $p\in(1,\infty)$, on strip-like domains $D$ form $\mathbb{R}^k\times\prod\limits_{i=1}^{n-k}(a_i,b_i)$. show that such are always maximally noncompact, is, their coincides with norms. Furthermore, we not only but also all strict $s$-numbers in question coincide prove maximal remains v...

In this article, we study the controllability of impulsive functional differential equations with nonlocal conditions. We establish sufficient conditions for controllability, via the measure of noncompactness and Mönch fixed point theorem.