Existence Results for Polyharmonic Boundary Value Problems in the Unit Ball by Sonia Ben Othman, Habib Mâagli, Malek Zribi

“…Our approach is based on estimates for the polyharmonic Green function on B with zero Dirichlet boundary conditions, including a 3G-theorem, which leeds to some useful properties on functions belonging to the Kato class.…”
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Global Existence and Blow-Up of Solutions to a Parabolic Nonlocal Equation Arising in a Theory of Thermal Explosion by Wenyuan Ma, Zhixuan Zhao, Baoqiang Yan

“…First, we prove a comparison principle for some kinds of semilinear parabolic equations under nonlinear boundary conditions; using it, we show a new theorem of subsupersolutions. Secondly, based on the new method of subsupersolutions, the existence of global solutions and blow-up solutions is presented for different values of p. …”
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On the Fuzzy Number Space with the Level Convergence Topology by J. J. Font, A. Miralles, M. Sanchis

“…We apply these results to give an Arzela-Ascoli theorem for the space of (𝔼1,τℓ)-valued continuous functions on a locally compact topological space equipped with the compact-open topology.…”
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Dynamical Analysis and Stabilizing Control of Inclined Rotational Translational Actuator Systems by Bingtuan Gao, Fei Ye

“…Consequently, a stabilizing controller is achieved directly based on the second Lyapunov stability theorem. Finally, numerical simulations are performed to verify the correctness and feasibility of our dynamical analysis and control design.…”
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Adaptive Integral Observer-Based Synchronization for Chaotic Systems with Unknown Parameters and Disturbances by Xiuchun Li, Jianhua Gu, Wei Xu

“…The analysis and proof are given by means of the Lyapunov stability theorem and Barbalat lemma. This approach has fewer constraints because many parameters related to chaotic system can be unknown, as shown in the paper. …”
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Fuzzy Hypervector Spaces by R. Ameri, O. R. Dehghan

“…Finally, a fuzzy quotient hypervector space is defined and an analogue of a consequence of the “fundamental theorem of homomorphisms” is obtained.…”
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The Eigenvalue Problem for Caputo Type Fractional Differential Equation with Riemann-Stieltjes Integral Boundary Conditions by Wenjie Ma, Yujun Cui

“…By using the Guo-Krasnoselskii’s fixed point theorem on cone and the properties of the Green’s function, some new results on the existence and nonexistence of positive solutions for the fractional differential equation are obtained.…”
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Finite Difference Method for Infection Model of HPV with Cervical Cancer under Caputo Operator by Bushra Bajjah, Mahmut Modanli

“…Generalized mean value theorem has been used to examine whether the infection model has a unique positive solution. …”
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Incompressible Schrödinger Flow with Heat-Transfer: An Introduction to the Analysis of Isotropic Fluid Dynamics in Sobolev Spaces for an Immersed Arbitrary Isothermal Geometry by Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales

“…The initial discoveries produce an important theorem that leads the name of the authors, allowing new and valuable insights into the effects of the isothermal body immersed in a fluid medium. …”
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A Novel Linear Active Disturbance Rejection Control Design for Air-Breathing Supersonic Vehicle Attitude System with Prescribed Performance by Chao Ming, Xiaoming Wang

“…On the basis of the Lyapunov stability theorem, the convergence and stability characteristics are both rigorously proved for the closed-loop system. …”
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A Perturbed Projection Algorithm with Inertial Technique for Split Feasibility Problem by Yazheng Dang, Yan Gao, Yanli Han

“…The results improve and extend the algorithms presented in Byrne (2002) and in Zhao and Yang (2005) and the related convergence theorem.…”
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Investigation of Aerodynamic Characteristics of Aircrafts in a Rarefied Gas Flow Using the Moment Method by Auzhan Sakabekov, Saltanat Madaliyeva, Ryskul Yergazina

“…This paper proves the existence and uniqueness of the solution of the abovementioned problem in the space of functions continuous in time and summable in the square by spatial variable. The theorem on the existence and uniqueness of a solution of the initial and boundary value problem for the moment system of equations in the third approximation is proved by the method of a priori estimation and using the Galerkin method and Tartar’s compensated compactness method.…”
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Equilibrium Further Studied for Combined System of Cournot and Bertrand: A Differential Approach by Bingyuan Gao, Yueping Du

“…The theory of spatial agglomeration and intermediate value theorem are introduced. In addition, the stability of equilibrium points is further illustrated on celestial bodies motion. …”
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A class of rings which are algebric over the integers by Douglas F. Rall

“…A well-known theorem of N. Jacobson states that any periodic associative ring is commutative. …”
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Mean-Square Convergence of Drift-Implicit One-Step Methods for Neutral Stochastic Delay Differential Equations with Jump Diffusion by Lin Hu, Siqing Gan

“…The applicability of the mean-square convergence theory is illustrated by the stochastic θ-methods and the balanced implicit methods. It is derived from Theorem 3.1 that the order of the mean-square convergence of both of them for NSDDEs with jumps is 1/2. …”
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Analysis to entity mobility models of wireless ad hoc networks by LIU Yan-tao1, AN Jian-ping2, LU Ji-hua2, LIU Heng2

“…Stationary speed distribution of random waypoint model,random direction model,and random walk model were analyzed by Palm calculus.The hypostasis of speed decay was proved to be the correlation between speed and dura-tion within any movement period.Stationary node distribution of random waypoint model and random direction model were discussed,respectively,by Palm calculus and geometric probability.It turned out that nodes in these two models tended to be non-uniform.Last,based on the central limit theorem,trace endpoints of random walk model in boundless regions was proved to be governed by normal distribution.As a result,random walk model based on time combines the strengths of entity mobility models on the performance of stationary speed distribution and node distribution,so it be-comes the most reasonable one.…”
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Estimates for the Green function and singular solutions for polyharmonic nonlinear equation by Imed Bachar, Habib Màagli, Syrine Masmoudi, Malek Zribi

“…We establish a new form of the 3G theorem for polyharmonic Green function on the unit ball of ℝn(n≥2) corresponding to zero Dirichlet boundary conditions. …”
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Triple Positive Solutions for Third-Order m-Point Boundary Value Problems on Time Scales by Jian Liu, Fuyi Xu

“…We obtain the existence of three positive solutions by using fixed-point theorem in cones. The conclusions in this paper essentially extend and improve the known results.…”
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Convergence of weighted sums of independent random variables and an extension to Banach space-valued random variables by W. J. Padgett, R. L. Taylor

“…This extension provides a convergence theorem that applies to stochastic processes which may be considered as random elements in function spaces.…”
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Empirical Likelihood Estimation for Population Pharmacokinetic Study Based on Generalized Linear Model by Fang-rong Yan, Jin-guan Lin, Yuan Huang, Jun-lin Liu, Tao Lu

“…A nonparametric version of the Wilk's theorem for the limiting distributions of the empirical likelihood ratio is derived. …”
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