This paper presents a mathematical analysis of the inverse problem concerning the recovery of two unknown potential coefficients in a coupled Schrödinger equations system, within a bounded domain of the Euclidean space Rn with Dirichlet boundary conditions. Our analysis relies on Neumann boundary measurements, where we establish under a geometric convexity assumption on the interior domain and weak regularity requirements for the data both the uniqueness property and Lipschitz stability for this inverse problem. The mathematical proof rests on two fundamental pillars: First, the proof of solution uniqueness is based on Carleman estimates specific to Schrödinger equations. Second, the proof of the stability result depends on a combination of (a) the aforementioned uniqueness result, and (b) an observability inequality.
In this paper, we present an extensive range of strong coupled fixed point solutions for ρ-F-contractive type covariant mappings in a Bipolar parametric metric space. Furthermore, we delve into several applications, including systems of non-linear Fredholm integral equations and homotopy. Additionally, we provide an example to illustrate our perspective.
In this study, we explore the presence of solutions for nonlocal initial value problems involving implicit differential equations featuring the Hilfer-Katugampola fractional derivative. We establish the Ulam-Hyers stability for the solutions of these equations within the weighted space Cħ,ρ[a,b]. To demonstrate our findings, we provide several illustrative examples.
In this paper, we present the concept of averaging Hom-associative algebras, which are Hom-associative algebras endowed with an averaging operator. We define representations and dual representations for these algebras without imposing any specific conditions. Subsequently, we develop a cohomology theory tailored to averaging Hom-associative algebras. We further explore both infinitesimal and formal deformation theories, demonstrating that the introduced cohomology serves as the deformation cohomology. Additionally, we define abelian extensions of averaging Hom-associative algebras and establish that the equivalence classes of such extensions correspond to elements in the second cohomology group.
This paper establishes fixed point results for interpolative contraction in elliptic-valued metric space with some applications. A supporting example is provided to verify the theoretical results. Furthermore, the paper explores practical applications of these findings by employing two-scale fractional differential equations together with the variational iteration method and a Poisson-type elliptic model to demonstrate their applicability and significance.
