A NEW GENERALIZATION OF GEORGE & VEERAMANI-TYPE FUZZY METRIC SPACE by A. Das, D. Barman, T. Bag

Subjects: “…𝑡-norm…”
Get full text

A Note on Confidence Interval for the Power of the One Sample 𝑡 Test by A. Wong

“…The method is then applied to the one-sample mean problem with unknown variance to obtain a (1−𝛾)100% confidence interval for the power of the Student's 𝑡-test that detects the difference (𝜇−𝜇0). …”
Get full text

Permanence of a Semi-Ratio-Dependent Predator-Prey System with Nonmonotonic Functional Response and Time Delay by Xuepeng Li, Wensheng Yang

“…Sufficient conditions for permanence of a semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay ̇𝑥1(𝑡)=𝑥1(𝑡)[𝑟1(𝑡)−𝑎11(𝑡)𝑥1(𝑡−𝜏(𝑡))−𝑎12(𝑡)𝑥2(𝑡)/(𝑚2+𝑥21(𝑡))],  ̇𝑥2(𝑡)=𝑥2(𝑡)[𝑟2(𝑡)−𝑎21(𝑡)𝑥2(𝑡)/𝑥1(𝑡)], are obtained, where 𝑥1(𝑡) and 𝑥2(𝑡) stand for the density of the prey and the predator, respectively, and 𝑚≠0 is a constant. 𝜏(𝑡)≥0 stands for the time delays due to negative feedback of the prey population.…”
Get full text

On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays by Jaromír Baštinec, Leonid Berezansky, Josef Diblík, Zdeněk Šmarda

“…New nonoscillation and oscillation criteria are derived for scalar delay differential equations ̇𝑥(𝑡)+𝑎(𝑡)𝑥(ℎ(𝑡))=0,𝑎(𝑡)≥0,ℎ(𝑡)≤𝑡,𝑡≥𝑡0, and ∑̇𝑥(𝑡)+𝑚𝑘=1𝑎𝑘(𝑡)𝑥(ℎ𝑘(𝑡))=0,𝑎𝑘(𝑡)≥0,ℎ𝑘(𝑡)≤𝑡, and 𝑡≥𝑡0, in the critical case including equations with several unbounded delays, without the usual assumption that the parameters 𝑎,ℎ,𝑎𝑘, and ℎ𝑘 of the equations are continuous functions. …”
Get full text

Oscillation Theorems for Second-Order Damped Nonlinear Differential Equations by Hui-Zeng Qin, Yongsheng Ren

“…We present new oscillation criteria for the differential equation of the form [𝑟(𝑡)𝑈(𝑡)]+𝑝(𝑡)𝑘2(𝑥(𝑡),𝑥(𝑡))|𝑥(𝑡)|𝜈𝑈(𝑡)+𝑞(𝑡)𝜙(𝑥(𝑔1(𝑡)),𝑥(𝑔2(𝑡)))𝑓(𝑥(𝑡))=0, where 𝑈(𝑡)=𝑘1(𝑥(𝑡),𝑥(𝑡))|𝑥(𝑡)|𝛼−1𝑥(𝑡), 𝛼≤𝛽,𝜈=(𝛽−𝛼)/(𝛼+1). …”
Get full text

Nonoscillatory Solutions of Second-Order Superlinear Dynamic Equations with Integrable Coefficients by Quanwen Lin, Baoguo Jia

“…The asymptotic behavior of nonoscillatory solutions of the superlinear dynamic equation on time scales (𝑟(𝑡)𝑥Δ(𝑡))Δ+𝑝(𝑡)|𝑥(𝜎(𝑡))|𝛾sgn𝑥(𝜎(𝑡))=0, 𝛾>1, is discussed under the condition that 𝑃(𝑡)=lim𝜏→∞∫𝜏𝑡𝑝(𝑠)Δ𝑠 exists and 𝑃(𝑡)≥0 for large 𝑡.…”
Get full text

Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory by Jing Chen, X. H. Tang

“…We study the existence and multiplicity of solutions for the following fractional boundary value problem: (𝑑/𝑑𝑡)((1/2)0𝐷𝑡−𝛽(𝑢′(𝑡))+(1/2)𝑡𝐷𝑇−𝛽(𝑢′(𝑡)))+∇𝐹(𝑡,𝑢(𝑡))=0,a.e.𝑡∈[0,𝑇],𝑢(0)=𝑢(𝑇)=0, where 𝐹(𝑡,⋅) are superquadratic, asymptotically quadratic, and subquadratic, respectively. …”
Get full text

Asymptotic Behaviour of a Two-Dimensional Differential System with a Finite Number of Nonconstant Delays under the Conditions of Instability by Zdeněk Šmarda, Josef Rebenda

“…The asymptotic behaviour of a real two-dimensional differential system ∑𝑥′(𝑡)=𝖠(𝑡)𝑥(𝑡)+𝑚𝑘=1𝖡𝑘(𝑡)𝑥(𝜃𝑘(𝑡))+ℎ(𝑡,𝑥(𝑡),𝑥(𝜃1(𝑡)),…,𝑥(𝜃𝑚(𝑡))) with unbounded nonconstant delays 𝑡−𝜃𝑘(𝑡)≥0 satisfying lim𝑡→∞𝜃𝑘(𝑡)=∞ is studied under the assumption of instability. …”
Get full text

Oscillation and Nonoscillation Criteria for Nonlinear Dynamic Systems on Time Scales by Shanliang Zhu, Chunyun Sheng

“…We consider the nonlinear dynamic system 𝑥Δ(𝑡)=𝑎(𝑡)𝑔(𝑦(𝑡)),𝑦Δ(𝑡)=−𝑓(𝑡,𝑥𝜎(𝑡)). …”
Get full text

Oscillation Theorems for Second-Order Half-Linear Advanced Dynamic Equations on Time Scales by Shuhong Tang, Tongxing Li, Ethiraju Thandapani

“…This paper is concerned with the oscillatory behavior of the second-order half-linear advanced dynamic equation (𝑟(𝑡)(𝑥Δ(𝑡))𝛾)Δ+𝑝(𝑡)𝑥𝛾(𝑔(𝑡))=0 on an arbitrary time scale 𝕋 with sup 𝕋=∞, where 𝑔(𝑡)≥𝑡 and ∫∞𝑡𝑜(Δ𝑠/(𝑟1/𝛾(𝑠)))<∞. …”
Get full text

Semiconservative Systems of Integral Equations with Two Kernels by N. B. Yengibaryan, A. G. Barseghyan

“…The solvability and the properties of solutions of nonhomogeneous and homogeneous vector integral equation ∫𝑓(𝑥)=𝑔(𝑥)+∞0∫𝑘(𝑥−𝑡)𝑓(𝑡)𝑑𝑡+0−∞𝑇(𝑥−𝑡)𝑓(𝑡)𝑑𝑡, where 𝐾, 𝑇 are 𝑛×𝑛 matrix valued functions, 𝑛≥1, with nonnegative integrable elements, are considered in one semiconservative (singular) case, where the matrix ∫𝐴=∞−∞𝐾(𝑥)𝑑𝑥 is stochastic one and the matrix ∫𝐵=∞−∞𝑇(𝑥)𝑑𝑥 is substochastic one. …”
Get full text

Semi-topological properties by Bhamini M. P. Nayar, S. P. Arya

Subjects: “…semi-open sets…”
Get full text

Properties of Third-Order Nonlinear Functional Differential Equations with Mixed Arguments by B. Baculíková

“…The aim of this paper is to offer sufficient conditions for property (B) and/or the oscillation of the third-order nonlinear functional differential equation with mixed arguments [𝑎(𝑡)[𝑥″(𝑡)]𝛾]′=𝑞(𝑡)𝑓(𝑥[𝜏(𝑡)])+𝑝(𝑡)ℎ(𝑥[𝜎(𝑡)]). …”
Get full text

Periodic Solutions for a Class of 𝑛-th Order Functional Differential Equations by Bing Song, Lijun Pan, Jinde Cao

“…We study the existence of periodic solutions for n-th order functional differential equations 𝑥(𝑛)∑(𝑡)=𝑛−1𝑖=0𝑏𝑖[𝑥(𝑖)(𝑡)]𝑘+𝑓(𝑥(𝑡−𝜏(𝑡)))+𝑝(𝑡). …”
Get full text

Perturbation Results and Monotone Iterative Technique for Fractional Evolution Equations by Jia Mu

“…We mainly study the fractional evolution equation in an ordered Banach space 𝑋𝐶𝐷𝑎0+𝑢(𝑡)+𝐴𝑢(𝑡)=𝑓(𝑡,𝑢(𝑡),𝐺𝑢(𝑡)) , 1<𝛼<2, 𝑢(0)=𝑥∈𝑋, 𝑢(0)=𝜃. …”
Get full text

Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals by Aneta Sikorska-Nowak

“…We prove existence theorems for integro-differential equations 𝑥Δ∫(𝑡)=𝑓(𝑡,𝑥(𝑡),𝑡0𝑘(𝑡,𝑠,𝑥(𝑠))Δ𝑠), 𝑥(0)=𝑥0, 𝑡∈𝐼𝑎=[0,𝑎]∩𝑇, 𝑎∈𝑅+, where 𝑇 denotes a time scale (nonempty closed subset of real numbers 𝑅), and 𝐼𝑎 is a time scale interval. …”
Get full text

Existence and Multiplicity of Solutions for Discrete Nonlinear Two-Point Boundary Value Problems by Jianmin Guo, Caixia Guo

“…By using Morse theory, the critical point theory, and the character of 𝐾1/2, we consider the existence and multiplicity results of solutions to the following discrete nonlinear two-point boundary value problem −Δ2𝑥(𝑘−1)=𝑓(𝑘,𝑥(𝑘)),𝑘∈ℤ(1,𝑇) subject to 𝑥(0)=0=Δ𝑥(𝑇), where 𝑇 is a positive integer, ℤ(1,𝑇)={1,2,…,𝑇},Δ is the forward difference operator defined by Δ𝑥(𝑘)=𝑥(𝑘+1)−𝑥(𝑘), and 𝑓∶ℤ(1,𝑇)×ℝ→ℝ is continuous. …”
Get full text

Positive Solutions for Singular Complementary Lidstone Boundary Value Problems by Fanglei Wang, Yukun An

“…By using fixed-point theorems of a cone, we investigate the existence and multiplicity of positive solutions for complementary Lidstone boundary value problems: (−1)𝑛𝑢(2𝑛+1)(𝑡)=ℎ(𝑡)𝑓(𝑢(𝑡)), in 0<𝑡<1, 𝑢(0)=0, 𝑢(2𝑖+1)(0)=𝑢(2𝑖+1)(1)=0, 0≤𝑖≤𝑛−1, where 𝑛∈𝑁.…”
Get full text

Bifurcation from Interval and Positive Solutions of a Nonlinear Second-Order Dynamic Boundary Value Problem on Time Scales by Hua Luo

“…Let 𝕋 be a time scale with 0,T∈𝕋. We give a global description of the branches of positive solutions to the nonlinear boundary value problem of second-order dynamic equation on a time scale 𝕋, uΔΔ(t)+f(t,uσ(t))=0,  t∈[0,T]𝕋,  u(0)=u(σ2(T))=0, which is not necessarily linearizable. …”
Get full text

Construction Solutions of PDE in Parametric Form by Alexandra K. Volosova, Konstantin Alexandrovich Volosov

“…In the case of three and more independent variables 𝑥,𝑦,𝑡,…, then it gives the possibility of expressing PDE second order as 𝐴𝑋=𝑏, if we do same compliment proposes. …”
Get full text