Subharmonics with Minimal Periods for Convex Discrete Hamiltonian Systems by Honghua Bin

“…By using variational methods and dual functional, we obtain that the system has a -periodic solution for each positive integer , and solution of system has minimal period as subquadratic growth both at 0 and infinity.…”
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Invariance principle for independent random variables with infinite variance by Mindaugas Juodis

“… A functional central limit theorem for self-normalized adaptive process U−1m,N ζn is considered, where Um,N is a sum of squares of block-sums of size m, as m and the number of blocks N = n/m tend to infinity. …”
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Expansion properties of Whitehead moves on cubic graphs by Grave de Peralta, Laura, Kolpakov, Alexander

“…Here, we prove that the outer-conductance of the graph of graphs tends to zero as the number of vertices tends to infinity. This answers a question of K. Rafi in the negative.…”
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Entire Blow-Up Solutions of Semilinear Elliptic Systems with Quadratic Gradient Terms by Yongju Yang, Xinguang Zhang

“…We establish the conditions on that ensure the existence of nonnegative radial solutions blowing up at infinity and also the conditions for bounded solutions on the entire space. …”
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An Improvement of the Differential Transformation Method and Its Application for Boundary Layer Flow of a Nanofluid by Abdelhalim Ebaid, Hassan A. El-Arabawy, Nader Y. Abd Elazem

“…The main advantage of the present technique is the complete avoidance of using Padé approximants to treat the infinity boundary conditions.…”
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Asymptotic behavior for a nonlinear viscoelastic problem with a velocity-dependent material density by Nasser-Eddine Tatar

“…We consider a nonlinear viscoelastic problem and prove that the solutions are uniformly bounded and decay exponentially to zero as time goes to infinity. This is established under weaker conditions on the relaxation function than the usually used ones. …”
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Applying the machine learning methods to determine the linear optics parameters in the ThomX collector ring by D. Klekots, O. Bezshyyko, L. Golinka-Bezshyyko, V. Kubytskyi, I. Chaikovska

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Global Existence and Asymptotic Behavior of Self-Similar Solutions for the Navier-Stokes-Nernst-Planck-Poisson System in ℝ3 by Jihong Zhao, Chao Deng, Shangbin Cui

“…For small initial data, the global existence, uniqueness, and asymptotic stability as time goes to infinity of self-similar solutions to the Cauchy problem of this system posed in the whole three dimensional space are proved in the function spaces of pseudomeasure type.…”
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Limit properties of rational Bézier curves with mixed weights(具有混合权函数的有理Bézier曲线的极限性质) by 魏琦文(WEI Qiwen), 刘向云(LIU Xiangyun), 吴金明(WU Jinming), 朱春钢(ZHU Chungang)

“…As the weight of a rational Bézier curve approaches infinity, the curve tends towards the corresponding control point. …”
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A New Result of Stability for Thermoelastic-Bresse System of Second Sound Related with Forcing, Delay, and Past History Terms by Djamel Ouchenane, Zineb Khalili, Fares Yazid, Mohamed Abdalla, Bahri Belkacem Cherif, Ibrahim Mekawy

“…We consider a one-dimensional linear thermoelastic Bresse system with delay term, forcing, and infinity history acting on the shear angle displacement. …”
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New Periodic Solutions for the Singular Hamiltonian System by Yi Liao

“…By use of the Cerami-Palais-Smale condition, we generalize the classical Weierstrass minimizing theorem to the singular case by allowing functions which attain infinity at some values. As an application, we study certain singular second-order Hamiltonian systems with strong force potential at the origin and show the existence of new periodic solutions with fixed periods.…”
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Multiple Solutions for the Asymptotically Linear Kirchhoff Type Equations on RN by Yu Duan, Chun-Lei Tang

“…We will show that if the nonlinearities are asymptotically linear at infinity and λ>0 is sufficiently small, the Kirchhoff type equations have at least two positive solutions. …”
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Granular media equation with double-well external landscape: limiting steady state by Tugaut, Julian

“…In this paper, we give a simple condition on the initial state of the granular media equation which ensures that the limit as the time goes to infinity is the unique steady state with positive center of mass. …”
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Oscillation and Asymptotic Behavior of Three-Dimensional Third-Order Delay Systems by Ahmed Abdulhasan Naeif, Hussain Ali Mohamad

“…Some sufficient conditions are obtained to ensure that every solution of the system is either oscillatory or nonoscillatory and converges to zero or diverges as t goes to infinity. A special technique is adopted to include all possible cases for all nonoscillatory solutions (NOSs). …”
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Painleve analysis of travelling wave solutions and analysis of energy estimates for a nonlinear Sobolev-type equation by A. I. Aristov

“…In many cases, energy estimates can be used to prove that the solution tends to infinity in finite time, while also providing an estimate for the latter. …”
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Global Existence and Uniform Energy Decay Rates for the Semilinear Parabolic Equation with a Memory Term and Mixed Boundary Condition by Zhong Bo Fang, Liru Qiu

“…Under suitable conditions, we prove the existence and uniqueness of global solutions and the energy functional decaying exponentially or polynomially to zero as the time goes to infinity by introducing brief Lyapunov function and precise priori estimates.…”
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Two Remarks on the Infinite Approximation of a Finite World in Economic Models by Shravan Luckraz

“…While the assumption of infinity is prevalent in almost every area of economics, for two well-known frameworks in decision theory, we note some fundamental differences between the finite versions and their infinite counterpart. …”
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Chaotic dynamics of string around charged black brane with hyperscaling violation by Da-Zhu Ma, Dan Zhang, Guoyang Fu, Jian-Pin Wu

“…The temperature plays the role of driving the closed string to escape to infinity. There is a threshold value z∗ = 2, below which the string is captured by the black brane no matter where the string is placed at the beginning. …”
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Bound chaotic photon orbits in a magnetized Kerr–Newman spacetime by Caiyu Liu, Daqi Yang, Xin Wu

“…There are three bound photon orbits, which neither fall into the black hole nor escape to infinity. They are stable circular orbits, bound quasiperiodic orbits and bound chaotic orbits. …”
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Weak cosmic censorship, trapped surfaces, and naked singularities for the Einstein vacuum equations by Shlapentokh-Rothman, Yakov

“…The weak cosmic censorship conjecture posits that, generically, all singularities in General Relativity arising from regular asymptotically flat initial data should have a complete future null infinity. While this conjecture remains wide open, it has inspired many mathematical works concerning topics such as trapped surface formation and the construction of naked singularities. …”
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