Abstract The theoretical approach of random impulsive stochastic integrodifferential equations (RISIDEs) with finite delay, noncompact semigroups, and resolvent operators in Hilbert space is investigated this article. Initially, a system proposed the existence mild solution for established using Mönch fixed-point theorem contemplating Hausdorff measures noncompactness. Then, stability results i...

We study the boundedness of the Hausdorff measure of the singular set of any solution for a semi-linear elliptic equation in general dimensional Euclidean space Rn. In our previous paper, we have clarified the structures of the nodal set and singular set of a solution for the semi-linear elliptic equation. In particular, we showed that the singular set is (n − 2)-rectifiable. In this paper, we ...

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.

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...

We investigate graph-directed iterated function systems in mixed Euclidean and p-adic spaces. Hausdorff measure and Hausdorff dimension in such spaces are defined, and an upper bound for the Hausdorff dimension is obtained. The relation between the Haar measure and the Hausdorff measure is clarified. Finally, we discus an example in R×Q2 and calculate upper and lower bounds for its Hausdorff di...

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.