Almost Surely Asymptotic Stability of Numerical Solutions for Neutral Stochastic Delay Differential Equations by Zhanhua Yu, Mingzhu Liu

“…We investigate the almost surely asymptotic stability of Euler-type methods for neutral stochastic delay differential equations (NSDDEs) using the discrete semimartingale convergence theorem. It is shown that the Euler method and the backward Euler method can reproduce the almost surely asymptotic stability of exact solutions to NSDDEs under additional conditions. …”
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Positive solutions of higher order quasilinear elliptic equations by Marcelo Montenegro

“…The basic ingredients are the maximum principle, Moser iterative scheme, an eigenvalue problem, a priori estimates by rescalings, sub/supersolutions, and Krasnosel'skiĭ fixed point theorem.…”
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Existence of Subharmonic Solutions for a Class of Second-Order p-Laplacian Systems with Impulsive Effects by Wen-Zhen Gong, Qiongfen Zhang, X. H. Tang

“…By using minimax methods in critical point theory, a new existence theorem of infinitely many periodic solutions is obtained for a class of second-order p-Laplacian systems with impulsive effects. …”
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Some Applications of New Complex Function Space Constructed by Different Weights and Exponents by Awad A. Bakery, Elsayed A. E. Mohamed

“…Finally, we introduced an extension of Caristi’s fixed point theorem on it.…”
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Existence for Eventually Positive Solutions of High-Order Nonlinear Neutral Differential Equations with Distributed Delay by Huanhuan Zhao, Youjun Liu, Jurang Yan

“…We use Lebesgue's dominated convergence theorem to obtain new necessary and sufficient condition for the existence of eventually positive solutions.…”
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Multiple Periodic Solutions of Delayed Predator-Prey Systems with Type IV Functional Responses on Time Scales by Shengbin Yu, Haihui Wu, Jiangbin Chen

“…With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the existence of multiple positive periodic solutions of delayed predator-prey systems with type IV functional responses on time scales. …”
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Existence of Solutions of a Nonlocal Elliptic System via Galerkin Method by Alberto Cabada, Francisco Julio S. A. Corrêa

“…By means of the Galerkin method and by using a suitable version of the Brouwer fixed-point theorem, we establish the existence of at least one positive solution of a nonlocal elliptic N-dimensional system coupled with Dirichlet boundary conditions.…”
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The Lω-Compactness in Lω-Spaces by Shui-Li Chen, Jin-Lan Huang

“…Finally, the Alexander ω-subbase lemma and the Tychonoff product theorem with respect to Lω-compactness are given.…”
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Multipliers on weighted Hardy spaces over certain totally disconnected groups by Toshiyuki Kitada

“…We first show an (H1,L1) multiplier result from which Onneweer's theorem follows. We also give an (H1,H1) multiplier result under a condition of Baernstein-Sawyer type.…”
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A New Hybrid Algorithm for λ-Strict Asymptotically Pseudocontractions in 2-Uniformly Smooth Banach Spaces by Xin-dong Liu, Shih-sen Chang

“…Using the metric projection, a strong convergence theorem is obtained in a uniformly convex and 2-uniformly smooth Banach spaces. …”
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Existence of a Short-Run Equilibrium of the Dixit-Stiglitz-Krugman Model by Minoru Tabata, Nobuoki Eshima

“…Applying the Kakutani fixed-point theorem to the set-valued operator, under the most general assumptions, we prove that the model has a short-run equilibrium.…”
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Approximate controllability for a class of fractional semilinear system with instantaneous and non-instantaneous impulses by Yunhao Chu, Yansheng Liu

“…By applying the Kuratowski measure of noncompactness and $ \rho $-set contractive fixed-point theorem, the results for the considered system were obtained. …”
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The Dirichlet Problem for elliptic equations in unbounded domains of the plane by Paola Cavaliere, Maria Transirico

“…In this paper we prove a uniqueness and existence theorem for the Dirichlet problem in W2,p for second order linear elliptic equations in unbounded domains of the plane. …”
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On the Deficiencies of Some Differential-Difference Polynomials by Xiu-Min Zheng, Hong Yan Xu

“…The characteristic functions of differential-difference polynomials are investigated, and the result can be viewed as a differential-difference analogue of the classic Valiron-Mokhon’ko Theorem in some sense and applied to investigate the deficiencies of some homogeneous or nonhomogeneous differential-difference polynomials. …”
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Existence and Uniqueness Results of Volterra–Fredholm Integro-Differential Equations via Caputo Fractional Derivative by Ameth Ndiaye, Fulgence Mansal

“…Then, another result that deals with the existence of at least one solution is delivered, and some sufficient conditions for this result are established by means of the fixed point theorem of Schaefer. Ulam stability of the solution is discussed before including an example to illustrate the results of the proposal.…”
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First-Order Three-Point Boundary Value Problems at Resonance Part III by Mesliza Mohamed, Bevan Thompson, Muhammad Sufian Jusoh

“…By employing the implicit function theorem, sufficient conditions for the existence of three-point boundary value problems are established.…”
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Synchronization of a Class of Chaotic Systems with Different Dimensions by Jiming Zheng, Juan Li

“…Secondly, based on Lyapunov stability theorem and adaptive control method, an adaptive feedback hybrid controller and parameter adaptive laws are designed to realize synchronization of uncertain chaotic systems with different dimensions. …”
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Positive Periodic Solutions in a Discrete Time Three Species Competition System by Changjin Xu, Yusen Wu

“…By using Gaines and Mawhin's continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive periodic solutions of the model are obtained.…”
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Mathematical Analysis for a Discrete Predator-Prey Model with Time Delay and Holling II Functional Response by Dehong Ding, Kui Fang, Yang Zhao

“…Applying Gaines and Mawhin’s continuation theorem of coincidence degree theory and the method of Lyapunov function, we obtain some sufficient conditions for the existence global asymptotic stability of positive periodic solutions of the model.…”
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Bifurcation Analysis in a Kind of Fourth-Order Delay Differential Equation by Xiaoqian Cui, Junjie Wei

“…Then the direction and stability of the Hopf bifurcation are determined, using the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the analytic results.…”
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