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>

THIRD-ORDER GENERALIZED DISCONTINUOUS IMPULSIVE PROBLEMS ON THE HALF-LINE

In this paper, we improve the existing results in the literature by presenting weaker sufficient conditions for the solvability of a third-order impulsive problem on the half-line, having generalized impulse effects. More precisely, our nonlinearities do not need to be positive nor sublinear and the monotone assumptions are local ones. Our method makes use of some truncation and perturbed techniques and on the equiconvergence at infinity and the impulsive points. The last section contains an application to a boundary layer flow problem over a stretching sheet with and without heat transfer.

Impulsive Problems for Fractional Differential Equations with Functional Boundary Value Conditions at Resonance

We establish novel results on the existence of impulsive problems for fractional differential equations with functional boundary value conditions at resonance with dim⁡Ker L=1. Our results are based on the degree theory due to Mawhin, which requires appropriate Banach spaces and suitable projection schemes.

Intervensi terhadap Anak Usia Dini yang Mengalami Gangguan ADHD Melalui Pendekatan Kognitif Perilaku dan Alderian Play Therapy

ADHD is a neurodevelopmental disorder in which a child presents a significant problem due to a lack of attention or hyperactivity-impulsivity. ADHD can interfere with the development of children in terms of cognitive, behavioral, socialization and communication. A common mistake that ADHD treatment through pharmacological therapy will eliminate all the symptoms of hyperactivity and impulsive problems in children with ADHD, but the use of ADHD drugs in the long term then it will affect the children. Another alternative for dealing with ADHD children using a counseling approach is behavioral cognitive behavioral approach and Adlerian play therapy.Understanding of behavioral cognitive approaches and Adlerian play therapy can help address early childhood problems especially those with ADHD disorders.