In this paper we consider a class of second-order neutral functional differential equations. Under certain conditions, we establish the existence of multiple periodic solutions by means of Z 2 group index theory and variational methods. The main result is also illustrated with an example.

In a recent study by Kim (Bull. Korean Math. Soc. 53(4):1149-1156, 2016 ) an attempt was made to examine some of the identities and properties that are related to the degenerate Carlitz q-Bernoulli numbers and polynomials. In our paper we define the modified degenerate q-Bernoulli numbers and polynomials. As part of this we investigate some of the identities and properties that...

By formulating a new contraction mapping on a product space, the authors originally employed Banach fixed point theorem to derive the LMI-based robust exponential stability criterion for impulsive BAM neural networks with distributed delays and uncertain parameters. Numerical example illuminates that the new criterion is not worse than the existing results derived by Lyapunov...

In this paper, we study the existence of a second-order impulsive differential equations depending on a parameter λ. By employing a critical point theorem, the existence of at least three solutions is obtained. MSC: 34A37, 34K10.

We study the solvability of a functional equation involving q-fractional integrals. Such an equation arises in the study of the spread of an infectious disease that does not induce permanent immunity. Our method is based on the noncompactness measure argument in a Banach algebra and an extension of Darbo’s fixed point theorem. MSC: 62P10, 26A33, 45G10.

Taking the stochastic effects on growth rate and harvesting effort into account, we propose a stochastic delay model of species in two habitats. The main aim of this paper is to investigate optimal harvesting and dynamics of the stochastic delay model. By using the stochastic analysis theory and differential inequality technology, we firstly obtain sufficient conditions for...

This paper is concerned with the problem of H ∞ state estimation problem for a class of delayed static neural networks. The purpose of the problem is to design a delay-dependent state estimator such that the dynamics of the error system is globally exponentially stable with a prescribed H ∞ performance. Some improved delay-dependent conditions are established by using delay...

This paper is concerned with qualitative properties of the evolutionary p-Laplacian population model with delay. We first establish the existence of solutions of the model by using the method of parabolic regularization and energy estimate and give the uniqueness by a recursive process. Then, combining the upper and lower solution method and the oscillation theory of functional...

In this paper, we deal with the asymptotics and oscillation of the solutions of higher-order nonlinear dynamic equations with Laplacian and mixed nonlinearities of the form { r n − 1 ( t ) ϕ α n − 1 [ ( r n − 2 ( t ) ( ⋯ ( r 1 ( t ) ϕ α 1 [ x Δ ( t ) ] ) Δ ⋯ ) Δ ) Δ ] } Δ + ∑ ν = 0 N p ν ( t ) ϕ γ ν ( x ( g ν ( t ) ) ) = 0 on an above-unbounded time scale. By using a generalized...

In this research, the existence of the solutions for an impulsive fractional differential equation of order q with mixed boundary conditions is studied by using some well-known fixed point theorems. At last, an example is presented to illustrate our results.

We investigate nonexistence results of nontrivial solutions of fractional differential inequalities of the form ( FS q m ) : { D 0 / t q x i − Δ H ( λ i x i ) ≥ | η | α i + 1 | x i + 1 | β i + 1 , ( η , t ) ∈ H N × ] 0 , + ∞ [ , 1 ≤ i ≤ m , x m + 1 = x 1 , where D 0 / t q is the time-fractional derivative of order q ∈ ( 1 , 2 ) in the sense of Caputo, Δ H is the Laplacian in the...

We consider a nonautonomous discrete competition system with nonlinear interinhibition terms and feedback controls. By constructing a suitable Lyapunov function, we obtain some criteria about the extinction of one of the two species and the corresponding feedback controls varieties. Our conclusions not only supplement but also improve some existing ones. Numerical simulations are...

It is well known that the set of positive solutions may contain crucial clues for the stationary patterns. In this paper, we consider a class of diffusive logistic equations with nonlocal terms subject to the Dirichlet boundary condition in a bounded domain. We study the existence of positive solutions under certain conditions on the parameters by using bifurcation theory...

This paper deals with the existence of mild solutions for the abstract fractional nonlocal evolution equations with noncompact semigroup in partially ordered Banach spaces. Under some mixed conditions, a group of sufficient conditions for the existence of abstract fractional nonlocal evolution equations are obtained by using a Krasnoselskii type fixed point theorem. The results...

Using height functions of the nonlinear term on some bounded sets and considering integrations of these height functions, we obtain the existence of positive solutions for a class of singular fractional differential equations with infinite-point boundary value conditions.

In this paper, by applying the generating function methods and summation transform techniques, we establish some new convolution identities for the Frobenius-Euler polynomials. It turns out that some well-known results are obtained as special cases. MSC: 11B68, 11S40, 05A19.

In this paper, we study the nonlocal fractional differential equation: { D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = 0 , u ( 1 ) = η u ( ξ ) , where 1 < α < 2 , 0 < ξ < 1 , η ξ α − 1 = 1 , D 0 + α is the standard Riemann-Liouville derivative, f : [ 0 , 1 ] × [ 0 , + ∞ ) → R is continuous. The existence and uniqueness of positive solutions are obtained by means...

In this paper, a delayed phytoplankton-zooplankton system with Crowley-Martin functional response is investigated analytically. We study the permanence and analyze the stability of the both boundary and positive equilibrium points for the system with delay as well as the system without delay. The global asymptotic stability is discussed by constructing a suitable Lyapunov...

Consider the difference equation [ Δ 3 f ( z ) Δ f ( z ) − 3 2 ( Δ 2 f ( z ) Δ f ( z ) ) 2 ] k = P ( z , f ( z ) ) Q ( z , f ( z ) ) , where P ( z , f ) and Q ( z , f ) are prime polynomials in f ( z ) with deg f P = p , deg f Q = q , and d = max { p , q } > 0 . We give the supremum of d, an estimation of the sum of Nevanlinna exceptional values of meromorphic solution f ( z ) of...

In this paper, a genetic oscillator model with time delay is discretized by the Euler method. The discrete oscillator model is discussed by using Neimark-Sacker bifurcation theory. The direction and the stability of the Neimark-Sacker bifurcation has been studied using the center manifold theorem and normal form theory. Numerical simulations illustrate the theoretical results.

This paper aims at proposing an observer-based T-S fuzzy singular system. Firstly, we give a general model of nonlinear singular systems. We use the T-S fuzzy control method to form a T-S fuzzy singular system and we give the augmented system and compact form of a T-S fuzzy singular system. Secondly, we design a T-S fuzzy observer for the augmented system. In order to prove the...

In this paper, we consider the existence and uniqueness of weak solutions for a class of fractional superdiffusion equations with initial-boundary conditions. For a multidimensional fractional drift superdiffusion equation, we just consider the simplest case with divergence-free drift velocity u ∈ L 2 ( Ω ) only depending on the spatial variable x. Finally, exploiting the...

We study the stability problem of mild solutions of impulsive stochastic differential equations driven by a fractional Brown motion with finite time-varying delay. The Hurst parameter H of the fractional Brown motion belongs to ( 1 2 , 1 ) . In terms of fractional power of operators and semigroup theory, we obtain sufficient conditions that guarantee the stability of the mild...

In this paper, the problem of delay-dependent stability is investigated for uncertain Markovian jump neural networks with leakage delay, two additive time-varying delay components, and nonlinear perturbations. The Markovian jumping parameters in the connection weight matrices and two additive time-varying delay components are assumed to be different in the system model, and the...