Existence of Almost Periodic Solutions for Impulsive Neutral Functional Differential Equations by Junwei Liu, Chuanyi Zhang

“…Our results are based on Krasnoselskii’s fixed-point theorem combined with an exponentially stable strongly continuous operator semigroup. An example is given to illustrate the theory.…”
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On the S-Invariance Property for S-Flows by Amin Saif, Adem Kılıçman

“…We define an equivalence relation on a topological space which is acted by topological monoid S as a transformation semigroup. Then, we give some results about the S-invariant classes for this relation. …”
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Exponential Attractor for Lattice System of Nonlinear Boussinesq Equation by Min Zhao, Shengfan Zhou

“…We first verify the Lipschitz continuity of the continuous semigroup associated with the system. Then, we provide an estimation of the tail of the difference between two solutions of the system. …”
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Ternary Weighted Function and Beurling Ternary Banach Algebra l1ω(S) by Mehdi Dehghanian, Mohammad Sadegh Modarres Mosadegh

“…Let S be a ternary semigroup. In this paper, we introduce our notation and prove some elementary properties of a ternary weight function ω on S. …”
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Optimal Control of Linear Impulsive Antiperiodic Boundary Value Problem on Infinite Dimensional Spaces by JinRong Wang, YanLong Yang

“…Using exponential stabilizability and discussing the impulsive evolution operators, without compactness and exponential stability of the semigroup governed by original principle operator, we present the existence of optimal controls. …”
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Existence Theorems for Fractional Semilinear Integrodifferential Equations with Noninstantaneous Impulses and Delay by Bo Zhu, Minhui Zhu

“…In this paper, we consider a class of fractional semilinear integrodifferential equations with noninstantaneous impulses and delay. By the semigroup theory and fixed point theorems, we establish various theorems for the existence of mild solutions for the problem. …”
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Fixed points via a generalized local commutativity by Gerald F. Jungck

“…Let g:X→X. The concept of a semigroup of maps which is nearly commutative at g is introduced. …”
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A New Result of Stability for Thermoelastic-Bresse System of Second Sound Related with Forcing, Delay, and Past History Terms by Djamel Ouchenane, Zineb Khalili, Fares Yazid, Mohamed Abdalla, Bahri Belkacem Cherif, Ibrahim Mekawy

“…Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove the well-posedness of the problem using the semigroup method, where an asymptotic stability result of global solution is obtained.…”
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On representation of solutions to the heat equation by Auscher, Pascal, Hou, Hedong

“…We propose a simple method to obtain semigroup representation of solutions to the heat equation using a local $L^2$ condition with prescribed growth and a boundedness condition within tempered distributions. …”
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Impulsive Fractional Semilinear Integrodifferential Equations with Nonlocal Conditions by Xue Wang, Bo Zhu

“…This paper is devoted to a class of impulsive fractional semilinear integrodifferential equations with nonlocal initial conditions. Based on the semigroup theory and some fixed point theorems, the existence theory of PC-mild solutions is established under the condition of compact resolvent operator. …”
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Exponential Attractors for Parabolic Equations with Dynamic Boundary Conditions by Zhao-hui Fan

“…First, we give the existence of the exponential attractor in by proving that the corresponding semigroup satisfies the enhanced flattering property. …”
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Stability on coupling SIR epidemic model with vaccination by Helong Liu, Houbao Xu, Jingyuan Yu, Guangtian Zhu

“…We assume that the instantaneous death and infection rates depend on the age. Applying semigroup theory and so forth, we investigate the existence of equilibria. …”
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Another special role of $ \mathrm{L}^\infty $-spaces-evolution equations and Lotz' theorem by Christian Budde

“…In this paper, we review the underappreciated theorem by Lotz that tells us that every strongly continuous operator semigroup on a Grothendieck space with the Dunford-Pettis property is automatically uniformly continuous. …”
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(λ,μ)-Fuzzy Version of Ideals, Interior Ideals, Quasi-Ideals, and Bi-Ideals by Yuming Feng, P. Corsini

“…We introduced (λ,μ)-fuzzy ideals, (λ,μ)-fuzzy interior ideals, (λ,μ)-fuzzy quasi-ideals, and (λ,μ)-fuzzy bi-ideals of an ordered semigroup and studied them. When λ=0 and μ=1, we meet the ordinary fuzzy ones. …”
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Necessary Conditions for Optimality for Stochastic Evolution Equations by AbdulRahman Al-Hussein

“…We achieve our results through the semigroup approach.…”
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On the Initial Value Problem of Stochastic Evolution Equations in Hilbert Spaces by Xuping Zhang, Yongxiang Li, Pengyu Chen

“…The present paper studies the initial value problem of stochastic evolution equations with compact semigroup in real separable Hilbert spaces. The existence of saturated mild solution and global mild solution is obtained under the situation that the nonlinear term satisfies some appropriate growth conditions. …”
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New Concepts on Module Arens Regularity for Module Banach Algebras by Omid Pourbahri Rahpeyma, Davood Ebrahimi Bagha, Ghasem Soleimani Rad

“…Then a new module structure on the semigroup algebra l1S as l1ES-module with nontrivial right and left module actions is constructed. …”
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On the H.-Q. Li inequality on step-two Carnot groups by Zhang, Ye

“…In this note we show that the gradient estimate of the heat semigroup, or more precisely the H.-Q. Li inequality, is preserved under tensorization, some suitable group epimorphism, and central sum. …”
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A Note on Impulsive Fractional Evolution Equations with Nondense Domain by Zufeng Zhang, Bin Liu

“…Some errors in the existing paper concerned with nondensely defined fractional differential equations are pointed out, and correct formula of integral solutions is established by using integrated semigroup and some probability densities. Sufficient conditions for the existence are obtained by applying the Banach contraction mapping principle. …”
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Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays by R. Sakthivel, P. Revathi, N. I. Mahmudov

“…A set of novel sufficient conditions are derived with the help of semigroup theory and fixed point technique for achieving the required result. …”
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