Stability analysis for $ (\omega, c) $-periodic non-instantaneous impulsive differential equations

<abstract><p>In this paper, the stability of $ (\omega, c) $-periodic solutions of non-instantaneous impulses differential equations is studied. The exponential stability of homogeneous linear non-instantaneous impulsive problems is studied by using Cauchy matrix, and some sufficient conditions for exponential stability are obtained. Further, by using Gronwall inequality, sufficient conditions for exponential stability of $ (\omega, c) $-periodic solutions of nonlinear noninstantaneous impulsive problems are established. Finally, some examples are given to illustrate the correctness of the conclusion.</p></abstract>

Linear PDE with constant coefficients

We discuss practical methods for computing the space of solutions to an arbitrary homogeneous linear system of partial differential equations with constant coefficients. These rest on the Fundamental Principle of Ehrenpreis–Palamodov from the 1960s. We develop this further using recent advances in computational commutative algebra.

Measurement of Cosmetic Purchasing Decisions Using Brand Image and Consumer Trust

This study aimed to measure the purchasing decisions of cosmetics using the brand image and consumer trust. This type of research is quantitative research and uses a sample of 70 respondents. The terms of the instrument test include the validity and reliability of the data. The analysis requirements used normal, homogeneous, linear, and regression significance tests. The data were analyzed using structural equations. The research findings show that brand image affects consumer trust, brand image affects purchasing decisions, and consumer trust also affects purchasing decisions.

Dynamic Bargaining and Time-Consistency in Linear-State and Homogeneous Linear-Quadratic Cooperative Differential Games

Three different solution concepts are reviewed and computed for linear-state and homogeneous linear-quadratic cooperative differential games with asymmetric players. Discount rates can be nonconstant and/or different. Special attention is paid to the issues of time-consistency, agreeability and subgame-perfectness, both from the viewpoint of sustainability of cooperation and from the credibility of the announced equilibrium strategies.

Some Properties on The [p,q]-Order of Meromorphic Solutions of Homogeneous and Non-homogeneous Linear Differential Equations With Meromorphic Coefficients

In the present paper, we investigate the $\left[p,q\right] $-order of solutions of higher order linear differential equations \begin{equation*} A_{k}\left(z\right) f^{\left( k\right) }+A_{k-1}\left( z\right) f^{\left(k-1\right)}+\cdots +A_{1}\left( z\right) f^{\prime }+A_{0}\left( z\right) f=0 \end{equation*} and \begin{equation*} A_{k}\left( z\right) f^{\left( k\right) }+A_{k-1}\left( z\right) f^{\left(k-1\right) }+\cdots +A_{1}\left( z\right) f^{\prime }+A_{0}\left( z\right) f=F\left( z\right), \end{equation*} where $A_{0}\left( z\right) ,$ $A_{1}\left( z\right) ,...,A_{k}\left(z\right) \not\equiv 0$ and $F\left( z\right) \not\equiv 0$ are meromorphic functions of finite $\left[ p,q\right] $-order. We improve and extend some results of the authors by using the concept $\left[ p,q\right] $-order.

Existence of solutions for the semilinear abstract Cauchy problem of fractional order

In this paper we establish the existence of solutions for the nonlinear abstract Cauchy problem of order α ∈ (1, 2), where the fractional derivative is considered in the sense of Caputo. The autonomous and nonautonomous cases are studied. We assume the existence of an α-resolvent family for the homogeneous linear problem. By using this α-resolvent family and appropriate conditions on the forcing function, we study the existence of classical solutions of the nonhomogeneus semilinear problem. The non-autonomous problem is discussed as a perturbation of the autonomous case. We establish a variation of the constants formula for the nonautonomous and nonhomogeneous equation.