The Range of the Spectral Projection Associated with the Dunkl Laplacian by Salem Ben Said, Hatem Mejjaoli

“…As an application, we provide a spectral version of the Paley-Wiener theorem for the Dunkl transform.…”
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On the Existence of Three Positive Solutions for a Caputo Fractional Difference Equation by Lili Kong, Huiqin Chen, Luping Li, Shugui Kang

“…In this paper, we introduce the application of three fixed point theorem by discussing the existence of three positive solutions for a class of Caputo fractional difference equation boundary value problem. …”
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Observability of Nonlinear Fractional Dynamical Systems by K. Balachandran, V. Govindaraj, M. Rivero, J. A. Tenreiro Machado, J. J. Trujillo

“…We study the observability of linear and nonlinear fractional differential systems of order 0<α<1 by using the Mittag-Leffler matrix function and the application of Banach’s contraction mapping theorem. Several examples illustrate the concepts.…”
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Positive Solutions for Sturm-Liouville Boundary Value Problems in a Banach Space by Hua Su, Lishan Liu, Yonghong Wu

“…The sufficient condition for the existence of positive solution is obtained by the fixed point theorem of strict set contraction operators in the frame of the ODE technique. …”
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Symmetry Analysis, Invariant Solutions, and Conservation Laws of Fractional KdV-Like Equation by Maria Ihsane El Bahi, Khalid Hilal

“…Finally, Ibragimov’s theorem has been employed to construct the conservation laws.…”
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Mean-Square Almost Periodic Solutions for Impulsive Stochastic Host-Macroparasite Equation on Time Scales by Pan Wang, Qingmei Lin, Yongkun Li

“…By use of the Banach fixed point theorem and Gronwall-Bellman’s inequality technique on time scales, we obtain the existence and exponential stability of mean-square almost periodic solutions for the host-macroparasite equation on time scales. …”
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Semianalytical Approach for the Approximate Solution of Delay Differential Equations by Xiankang Luo, Mustafa Habib, Shazia Karim, Hanan A. Wahash

“…The beauty of this approach is that it does not need to compute the values of the Lagrange multiplier as in the variational iteration method, and also, there is no need to implement the convolution theorem as in the Laplace transform. The main purpose of this scheme is to reduce the less computational work and the error analysis of the problems than others studied in the literature. …”
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On Perturbations of Generators of C0-Semigroups by Martin Adler, Miriam Bombieri, Klaus-Jochen Engel

“…We present a perturbation result for generators of C0-semigroups which can be considered as an operator theoretic version of the Weiss-Staffans perturbation theorem for abstract linear systems. The results are illustrated by applications to the Desch-Schappacher and the Miyadera-Voigt perturbation theorems and to unbounded perturbations of the boundary conditions of a generator.…”
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Dynamical Behaviors of a Stage-Structured Predator-Prey Model with Harvesting Effort and Impulsive Diffusion by Lingzhi Huang, Zhichun Yang

“…By the impulsive comparison theorem and the discrete dynamical system determined by the stroboscopic map, we obtain some sufficient conditions on the existence and global attractiveness of predator-eradicated periodic solution for the system. …”
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𝑊𝟐,𝟐 A Priori Bounds for a Class of Elliptic Operators by Sara Monsurrò, Maria Salvato, Maria Transirico

“…We deduce a uniqueness and existence theorem for the related Dirichlet problem in some weighted Sobolev spaces on unbounded domains.…”
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Periodic Points of Asymmetric Bernoulli Shifts by Yong-Guo Shi, Kai Chen, Wei Liao

“…It is well-known that Sharkovskii’s theorem gives a complete structure of periodic order for a continuous self-map on a closed bounded interval. …”
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A Cantilever Beam Problem with Small Deflections and Perturbed Boundary Data by Ammar Khanfer, Lazhar Bougoffa

“…By determining appropriate values of λ and estimates for perturbation measurements on the boundary data, we establish an existence theorem for the problem under integral boundary conditions u0=u′0=∫01pxuxdx,u″1=u′′′1=∫01qxu″xdx, where p,q∈L10,1, and f is continuous on 0,1×0,∞×0,∞×−∞,0×−∞,0.…”
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Dynamics of a Computer Virus Propagation Model with Delays and Graded Infection Rate by Zizhen Zhang, Limin Song

“…In succession, direction and stability of the Hopf bifurcation when the two delays are not equal are determined by using normal form theory and center manifold theorem. Finally, some numerical simulations are also carried out to justify the obtained theoretical results.…”
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Permanence and Positive Periodic Solutions of a Discrete Delay Competitive System by Wenjie Qin, Zhijun Liu

“…When the system is periodic, by using the continuous theorem of coincidence degree theory and constructing a suitable Lyapunov discrete function, sufficient conditions which guarantee the existence and global attractivity of positive periodic solutions are obtained. …”
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Globally Exponential Stability of Periodic Solutions to Impulsive Neural Networks with Time-Varying Delays by Yuanfu Shao, Changjin Xu, Qianhong Zhang

“…By using Schaeffer's theorem and Lyapunov functional, sufficient conditions of the existence and globally exponential stability of positive periodic solution to an impulsive neural network with time-varying delays are established. …”
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Notes on channel capacity per unit cost by TIAN Da-gang

“…For the computation of the capacity per unit cost,an extension of the basic theorem connect the capacity per unit cost with the capacity-cost function was made,and the single peak of the generalized capacity-cost function per unit cost was proved.Then,an algorithm to locate the optimal point of the generalized capacity-cost function per unit cost based on the single peak of the function was proposed.Meanwhile,it was proved that the computation of the capac-ity-cost function,which is a constrained channel capacity issue,can be expressed as a convex optimization,to which the objective function is self-concordant.The algorithm and its computational complexity were given.…”
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A Class of Iterative Nonlinear Difference Inequality with Weakly Singularity by Chunmiao Huang, Wu-Sheng Wang, Xiaoliang Zhou

“…We discuss a class of new nonlinear weakly singular difference inequality, which is solved by change of variable, discrete Hölder inequality, discrete Jensen inequality, the mean-value theorem for integrals and amplification method, and Gamma function. …”
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Error Analysis of Galerkin's Method for Semilinear Equations by Tadashi Kawanago

“…The derivation of our results is, however, different from the discussion in his paper and is essentially based on the convergence theorem of Newton’s method and some techniques for deriving it. …”
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On the Approximation Properties of q−Analogue Bivariate λ-Bernstein Type Operators by Edmond Aliaga, Behar Baxhaku

“…For the first operators, we state the Volkov-type theorem and we obtain a Voronovskaja type and investigate the degree of approximation by means of the Lipschitz type space. …”
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Periodic Property and Asymptotic Behavior for a Discrete Ratio-Dependent Food-Chain System with Delays by Changjin Xu, Peiluan Li, Maoxin Liao

“…By using Gaines and Mawhin’s continuation theorem of coincidence degree theory and the method of Lyapunov function, a set of sufficient conditions for the existence of positive periodic solutions and global asymptotic stability of the model are established.…”
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