Stochastically Ultimate Boundedness and Global Attraction of Positive Solution for a Stochastic Competitive System by Shengliang Guo, Zhijun Liu, Huili Xiang

“…We first show that the positive solution of the above system does not explode to infinity in a finite time, and the existence and uniqueness of positive solution are discussed. …”
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Center problem for quartic differential systems with an affine invariant straight line of maximal multiplicity by Olga Vacaraș

“…In this paper the quartic differential systems with a center-focus critical point and non-degenerate infinity are examined. We show that in this family the maximal multiplicity of an affine invariant straight line is six. …”
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Multiplicity of Solutions for a Class of Fourth-Order Elliptic Problems with Asymptotically Linear Term by Qiong Liu, Dengfeng Lü

“…We study the following fourth-order elliptic equations: Δ2𝑢+𝑎Δ𝑢=𝑓(𝑥,𝑢),𝑥∈Ω,𝑢=Δ𝑢=0,𝑥∈𝜕Ω, where Ω⊂ℝ𝑁 is a bounded domain with smooth boundary 𝜕Ω and 𝑓(𝑥,𝑢) is asymptotically linear with respect to 𝑢 at infinity. Using an equivalent version of Cerami's condition and the symmetric mountain pass lemma, we obtain the existence of multiple solutions for the equations.…”
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Eigenvalue problems for a quasilinear elliptic equation on ℝN by Marilena N. Poulou, Nikolaos M. Stavrakakis

“…We prove the existence of a simple, isolated, positive principal eigenvalue for the quasilinear elliptic equation −Δpu=λg(x)|u|p−2u, x∈ℝN, lim|x|→+∞u(x)=0, where Δpu=div(|∇u|p−2∇u) is the p-Laplacian operator and the weight function g(x), being bounded, changes sign and is negative and away from zero at infinity.…”
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Evolutionary equation of inertial waves in 3-D multiply connected domain with Dirichlet boundary condition by Pavel A. Krutitskii

“…All results hold for interior domains and for exterior domains with appropriate conditions at infinity.…”
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Mathematical Modeling of Eigenvibrations of the Shallow Shell with an Attached Oscillator by D. M. Korosteleva, S. I. Solov’ev

“…It was established that there exist a sequence of positive eigenvalues of finite multiplicity with a limit point at infinity and the corresponding complete orthonormal system of eigenvectors. …”
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Convex dynamics in Hele-Shaw cells by Dmitri Prokhorov, Alexander Vasil'ev

“…We study geometric properties of a contracting bubble driven by a homogeneous source at infinity and surface tension. The properties that are preserved during the time evolution are under consideration. …”
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On-Line Selection of c-Alternating Subsequences from a Random Sample by Robert W. Chen, Larry A. Shepp, Justín Ju-Chen Yang

“…We also give the optimal selection rate when the sample size goes to infinity.…”
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Spatial behavior for the quasi-static heat conduction within the second gradient of type Ⅲ by Jincheng Shi, Shuman Li, Cuntao Xiao, Yan Liu

“…When the distance tends to infinity, the energy either grows exponentially or decays exponentially. …”
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Large Time Behavior of the Vlasov-Poisson-Boltzmann System by Li Li, Shuilin Jin, Li Yang

“…To be precise, we prove that when time goes to infinity, the solution of VPB system tends to global Maxwellian state in a rate Ot−∞, by using a method developed for Boltzmann equation without force in the work of Desvillettes and Villani (2005). …”
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UV-finite “old” conformal bootstrap on AdS: scalar case by Boris L. Altshuler

“…Abstract The double-trace from UV to IR flow subtraction of infinities used earlier for the UV-convergent calculations of the Witten tadpole diagrams being applied to the bubble self-energy diagrams gives for them the amazingly simple expressions in case of the four- dimensional boundary space. …”
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Existence of nodal solutions to some nonlinear boundary value problems for ordinary differential equations of fourth order by Ziyatkhan Aliyev, Yagut Aliyeva

“…To do this, we first study the global bifurcation of solutions from zero and infinity of the corresponding nonlinear eigenvalue problems in classes with a fixed oscillation count. …”
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On a non-self adjoint expansion formula by D. Naylor

“…This paper develops a formula of inversion for an integral transform of the kind similar to that associated with the names of Kontorovich and Lebedev except that the kernel involves the Neumann function Yu(kr) and the variable r varies over the infinite interval a≤r<∞ where a>0 The transform is useful in the investigation of functions that satisfy the Helmholtz equation and a condition of radiation at infinity. The formula established is expressed entirely in terms of series expansions and replaces earlier inversion formulas that require the evaluation of contour integrals.…”
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The Multivariate Müntz-Szasz Problem in Weighted Banach Space on Rn by Xiangdong Yang

“…The completeness of monomials {tλk} in Cα is investigated, where Cα is the weighted Banach spaces which consist of complex continuous functions f defined on Rn with f(t) exp(-α(t)) vanishing at infinity in the uniform norm.…”
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Square-free numbers in the intersection of Lehmer set and Piatetski-Shapiro sequence by Zhao Xiaoqing, Yi Yuan

“…By employing additive character properties to transform congruence equations and applying Kloosterman sums and methods of exponential sums, we derive a sharp asymptotic formula as $ q $ approaches infinity, which is significant for understanding the distribution properties of the Lehmer problem.…”
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On the structure of ionizing shock waves in magnetofluiddynamics by A. Aghajani, M. Hesaaraki

“…In this paper, we show that for the above electrical conductivity as well as for limiting cases, that is, when this coefficient is zero ahead of the shock and/or is infinity behind it, ionizing fast, slow, switch-on and switch-off shocks admit structure. …”
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Diagnostic Validity of Clinical Signs Associated with a Large Exophoria at Near by Pilar Cacho-Martínez, Ángel García-Muñoz, María Teresa Ruiz-Cantero

“…Using the cut-offs obtained with ROC analysis, the best diagnostic validity was obtained for the combination of NPC recovery and BAF (S  =  0.77, Sp = 1, LR+ = value tending to infinity, LR− = 0.23) and the combination of NPC break and recovery with BAF (S  =  0.73, Sp = 1, LR+ = tending to infinity, LR− = 0.27). …”
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Optimization of hydrothermal performance in industrial heat sinks with innovative perforated pin fin designs: A numerical approach by Fatema-Tuj Zohora, Mohammad Rejaul Haque, Nabil Mohammad Chowdhury, Mostafa Kamal Fahad, Nowroze Farhan Ifraj

“…Furthermore, the copper-diamond composite, which was placed on an infinity loop-shaped pin fin and had elliptical perforations, yielded a 144 % increase in HTPF when the Re is 44502. …”
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Existence of Homoclinic Orbits for a Class of Asymptotically p-Linear Difference Systems with p-Laplacian by Qiongfen Zhang, X. H. Tang

“…By applying a variant version of Mountain Pass Theorem in critical point theory, we prove the existence of homoclinic solutions for the following asymptotically p-linear difference system with p-Laplacian Δ(|Δu(n-1)|p-2Δu(n-1))+∇[-K(n,u(n))+W(n,u(n))]=0, where p∈(1,+∞), n∈ℤ, u∈ℝN, K,W:ℤ×ℝN→ℝ are not periodic in n, and W is asymptotically p-linear at infinity.…”
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Uniform Energy Decay Rates for the Fuzzy Viscoelastic Model with a Nonlinear Source by Fengyun Zhang

“…Under weak assumptions of the function gt, with the aid of Mathematica software, the computational technique is used to construct the auxiliary functionals and precise priori estimates. As time goes to infinity, we prove that the solution is global and energy decays to zero in two different ways: the exponential form and the polynomial form.…”
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