Revistas académicas de la Universidad Católica del Norte
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Cayley fuzzy graph representations of groups with emphasis on subgroup and left coset hierarchies
No full textExistence of solutions for Caputo-Hadamard problems of fractional differential equations involving p-Laplacian operator with integral boundary conditions: Existence of solutions for Caputo-Hadamard problems
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Compact operators
No full textWe give a characterization in terms of the transpose operator for a continuous linear operator between locally convex spaces to map bounded sets into relatively weakly compact [relatively compact, precompact] sets. Our results give a known characterization for compact operators between Banach spaces
Instability in nonlinear Schrödinger breathers
No full textWe consider the focusing Nonlinear Schrödinger equation posed on the one dimensional line, with nonzero background condition at spatial infinity, given by a homogeneous plane wave. For this problem of physical interest, we study the initial value problem for perturbations of the background wave in Sobolev spaces. It is well-known that the associated linear dynamics for this problem describes a phenomenon known in the literature as modulational instability, also recently related to the emergence of rogue waves in ocean dynamics. In qualitative terms, small perturbations of the background state increase its size exponentially in time. In this paper we show that, even if there is no time decay for the linear dynamics due to the modulationally unstable regime, the equation is still locally well-posed in Hs, s > 1/2. We apply this result to give a rigorous proof of the unstable character of two well-known NLS solutions: the Peregrine and Kuznetsov-Mabreathers.  
On the Common Spectral Properties among Bounded Linear Operators
No full textIn the context of , and be bounded linear operators on Banach space satisfying the following equations:\In this note we study common spectral properties for (resp. ) and (resp. ). Then we extend Cline's formula and Jacobson’s lemma for the Drazin ( resp generalized Drazin, resp generalized Drazin-Riesz) invertibility. Additionally, the study provides some others results linear operators in Banach spaces
Boundedness Results for Solutions of Certain Second Order Non-Autonomous Ordinary Differential Equations
No full textExistence and Controllability Results for Neutral Integro-Differential Equations with State Dependent Delay
No full textThe objective of our research is to investigate the existence and controlability of solutions for neutal integro-differential equations with state-dependent delays. We employ fixed point theorem to establish the existence of these solutions, while also utilizing the concept of measures of noncompactness. In the last section, we give an example to show that the assumed conditions can be verified and to illustrate our results
Existence Results for Nonlinear Sequential Hybride Fractional Differential Equation based on Dhage’s Fixed Point Theorem
No full text This paper studies the existence of solution of hybride fractional differential equation with hybride boundary conditios were ivestigation by the Dhage’s fixed theorem. Additionally, the U.H technique is employed to verify the stabiliy of this solution. The stady is concluded whit two examples that illustrate the pratical application of the theorecal results.