Stability and Bifurcation for a Delayed Diffusive Two-Zooplankton One-Phytoplankton Model with Two Different Functions by Xin-You Meng, Li Xiao

“…The explicit formulas to determine the properties of Hopf bifurcation are given by the method of the normal form theory and center manifold theorem for partial functional differential equations. …”
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Nonzero-Sum Stochastic Differential Game between Controller and Stopper for Jump Diffusions by Yan Wang, Aimin Song, Cheng-De Zheng, Enmin Feng

“…Furthermore, we apply the verification theorem to characterize Nash equilibrium of the game in a specific example.…”
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Automatic proof of resistance of denial of service attacks in protocols by Bo MENG, Wei HUANG, De-jun WAND, Fei SHAO

“…First,the applied PI calculus was extended from two aspects:attacker contexts and process expression,then from the view of protocol state,the protocols were modeled with the extended applied PI calculus and a automatic method of proof of resistance of denial of service attacks based on theorem proof with first order theorem prover ProVerif was presented,finally resistance of denial of service attacks in JFK protocol and IEEE 802.11 four-way handshake protocol were analyzed.The results obtained are that JFK protocol is resistance of denial of service attack and IEEE 802.11 four-way handshake protocol is not.At the same time a new al of service attack in IEEE 802.11 four-way handshake protocol was found.The methods to prevent resistance of denial of service attacks in IEEE 802.11 four-way handshake protocol were proposed.…”
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Properties and for Bounded Linear Operators by M. H. M. Rashid

“…We shall consider properties which are related to Weyl type theorem for bounded linear operators , defined on a complex Banach space . …”
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Multiple Solutions for Second-Order Sturm–Liouville Boundary Value Problems with Subquadratic Potentials at Zero by Dan Liu, Xuejun Zhang, Mingliang Song

“…We deal with the following Sturm–Liouville boundary value problem: −Ptx′t′+Btxt=λ∇xVt,x,  a.e. t∈0,1x0cos  α−P0x′0sin  α=0x1cos  β−P1x′1sin  β=0 Under the subquadratic condition at zero, we obtain the existence of two nontrivial solutions and infinitely many solutions by means of the linking theorem of Schechter and the symmetric mountain pass theorem of Kajikiya. …”
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A property of L−L integral transformations by Yu Chuen Wei

“…In addition, this paper gives a theorem that is an improvement of a theorem that is proved by J. …”
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Multiple Solutions to Fractional Difference Boundary Value Problems by Huiqin Chen, Yaqiong Cui, Xianglan Zhao

“…Based on the Krasnosel’skiǐ theorem and the Schauder fixed point theorem, we establish some conditions on f which are able to guarantee that this FBVP has at least two positive solutions and one solution, respectively. …”
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Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse by Zhenguo Luo, Liping Luo, Yunhui Zeng

“…By using a fixed point theorem of strict-set-contraction, which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory for k-set contraction, we established some new criteria for the existence of positive periodic solution of the following generalized neutral delay functional differential equation with impulse: x'(t)=x(t)[a(t)-f(t,x(t),x(t-τ1(t,x(t))),…,x(t-τn(t,x(t))),x'(t-γ1(t,x(t))),…,x'(t-γm(t,x(t))))],  t≠tk,  k∈Z+;  x(tk+)=x(tk-)+θk(x(tk)),  k∈Z+. …”
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On Some Fixed Point Results in E−Fuzzy Metric Spaces by Rachid Mecheraoui, Zoran D. Mitrović, Vahid Parvaneh, Hassen Aydi, Naeem Saleem

“…In the existing literature, Banach contraction theorem as well as Meir-Keeler fixed point theorem were extended to fuzzy metric spaces. …”
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Estimating Vehicle Stability Region Based on Energy Function by Yu-guang Yan, Hong-guo Xu, Hong-fei Liu

“…By establishing energy function for vehicle system, the vehicle’s stability region in 20 m/s was estimated based on Lyapunov theorem and vehicle system characteristics. Vehicle test in the same condition shows that the calculated stability region defined by Lyapunov and system stability theorem has good effect on characterized vehicle stability and it could be a valuable reference for vehicle stability evaluation.…”
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Contraction Mapping Theory and Approach to LMI-Based Stability Criteria of T-S Fuzzy Impulsive Time-Delays Integrodifferential Equations by Ruofeng Rao, Shouming Zhong

“…In this paper, Banach fixed point theorem is employed to derive LMI-based exponential stability of impulsive Takagi-Sugeno (T-S) fuzzy integrodifferential equations, originated from Cohen-Grossberg Neural Networks (CGNNs). …”
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Calculus Rules for V-Proximal Subdifferentials in Smooth Banach Spaces by Messaoud Bounkhel

“…They proved, in p-uniformly convex and q-uniformly smooth Banach spaces, the density theorem for the new concepts of proximal subdifferential and various important properties for both proximal subdifferential concepts and the proximal normal cone concept. …”
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Study on Stochastic Linear Quadratic Optimal Control with Quadratic and Mixed Terminal State Constraints by Yang Hongli

“…By means of the Lagrangian multiplier theorem and Riesz representation theorem, the main result given in this paper is the necessary condition for indefinite stochastic LQ control with quadratic and mixed terminal equality constraints. …”
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On the existence of solutions of the system of nonlinear quasi-mixed equilibrium problems and their stability of the procedure scheme by Satit Saejung

“…Lett. 24:308–313, 2011), utilizing Banach’s fixed point theorem. This result remains valid under weaker assumptions through the product space approach. …”
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Three-Point Boundary Value Problems of Nonlinear Second-Order q-Difference Equations Involving Different Numbers of q by Thanin Sitthiwirattham, Jessada Tariboon, Sotiris K. Ntouyas

“…By using a variety of fixed point theorems (such as Banach’s contraction principle, Boyd and Wong fixed point theorem for nonlinear contractions, Krasnoselskii’s fixed point theorem, and Leray-Schauder nonlinear alternative) and Leray-Schauder degree theory, some new existence and uniqueness results are obtained. …”
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Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions by Mısır J. Mardanov, Yagub A. Sharifov, Kamala E. Ismayilova

“…The Banach fixed point theorem is used to prove the existence and uniqueness of a solution of the problem and Schaefer’s fixed point theorem is used to prove the existence of a solution of the problem under consideration. …”
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Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System by Muhammad Marwan, Gauhar Ali, Ramla Khan

“…This work identifies the influence of chaos theory on fractional calculus by providing a theorem for the existence and stability of solution in fractional-order gyrostat model with the help of a fixed-point theorem. …”
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Investigation of a Mild Solution to Coupled Systems of Impulsive Hybrid Fractional Differential Equations by Mohamed Hannabou, Hilal Khalid

“…We used the classical fixed-point theorems such as the Banach fixed-point theorem and Leray–Schauder alternative fixed-point theorem for existence results. …”
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Research of the Conceptual Design of Dump Truck Drive Axle Housing based on Space Narrowing Methodology by Li Meng

“…The results show that,through space narrowing theory and interval propagation theorem,the concept design of dump truck drive axle housing change interval of main parameters is significantly reduced,the method can eliminate the uncertain information of initial design space,and the rationality of the optimization result is verified by finite element method.…”
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N-topo nilpotency in fuzzy neighborhood rings by T. M. G. Ahsanullah, Fawzi Al-Thukair

“…This leads us to prove a characterization theorem which says that if a fuzzy neighborhood ring on a division ring is Wuyts-Lowen WNT2 and locally inversely bounded, then the fuzzy neighborhood ring is a fuzzy neighborhood division ring. …”
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