Nonlinear Dynamic Analysis of the Cutting Process of a Nonextensible Composite Boring Bar by Bole Ma, Yongsheng Ren

“…The motion equation of nonlinear chatter of the cutting system is derived based on the Hamilton principle. The partial differential equation of motion is discretized using the Galerkin method to obtain a 1-dof nonlinear ordinary differential equation in a generalized coordinate system. …”
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A Computational Model for q-Bernstein Quasi-Minimal Bézier Surface by Daud Ahmad, M. Khalid Mahmood, Qin Xin, Ferdous M. O. Tawfiq, Sadia Bashir, Arsha Khalid

“…Instead of solving the partial differential equation, we can find the optimal conditions for which the surface is the extremal of the Dirichlet functional. …”
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Principal Parametric Resonance of Axially Accelerating Viscoelastic Beams: Multi-Scale Analysis and Differential Quadrature Verification by Li-Qun Chen, Hu Ding, C.W. Lim

“…The transverse motion can be governed by a non-linear partial-differential equation or a non-linear integro-partial-differential equation. …”
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Approximation of Analytic Functions by Bessel's Functions of Fractional Order by Soon-Mo Jung

“…We will solve the inhomogeneous Bessel's differential equation x2y″(x)+xy′(x)+(x2-ν2)y(x)=∑m=0∞amxm, where ν is a positive nonintegral number and apply this result for approximating analytic functions of a special type by the Bessel functions of fractional order.…”
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A New Proof of Central Limit Theorem for i.i.d. Random Variables by Zhaojun Zong, Feng Hu

“…Our main tool is the viscosity solution theory of partial differential equation (PDE).…”
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Existence and Uniqueness of Solutions for a Fractional Order Antiperiodic Boundary Value Problem with a p-Laplacian Operator by Ruihui Huang

“…We study the existence and uniqueness of solutions for a class of antiperiodic boundary value problems of the fractional differential equation with a p-Laplacian operator. Based on the Leray-Schauder nonlinear alternative, several sufficient conditions of the existence and uniqueness of solution of the above problem are established. …”
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A Predator-Prey Gompertz Model with Time Delay and Impulsive Perturbations on the Prey by Jianwen Jia, Chunhua Li

“…With the theory on the delay functional and impulsive differential equation, we obtain the appropriate condition for the permanence of the system.…”
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On Multiple Positive Solutions for Singular Fractional Boundary Value Problems with Riemann-Stieltjes Integrals by Lufeng Gu, Qiuyan Zhong, Zhuyan Shao

“…In this paper, the existence result of at least two positive solutions is obtained for a nonlinear Riemann-Liouville fractional differential equation subject to nonlocal boundary conditions, where fractional derivatives and Riemann-Stieltjes integrals are involved. …”
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Solvability of Three-Point Boundary Value Problems at Resonance with a p-Laplacian on Finite and Infinite Intervals by Hairong Lian, Patricia J. Y. Wong, Shu Yang

“…Three-point boundary value problems of second-order differential equation with a p-Laplacian on finite and infinite intervals are investigated in this paper. …”
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Spatial Dynamics for a Generalized Solow Growth Model by Yue Zhong, Wenyi Huang

“…The explicit solutions of the growth model, which is expressed by a differential equation with corresponding boundary conditions, are employed to illustrate the spatial dynamics of the model in different economic regions. …”
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The (G′/G)-Expansion Method and Its Application for Higher-Order Equations of KdV (III) by Huizhang Yang, Wei Li, Biyu Yang

“…New exact traveling wave solutions of a higher-order KdV equation type are studied by the (G′/G)-expansion method, where G=G(ξ) satisfies a second-order linear differential equation. The traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions, and the rational functions. …”
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An oriented coincidence index for nonlinear Fredholm inclusions with nonconvex-valued perturbations by Valeri Obukhovskii, Pietro Zecca, Victor Zvyagin

“…An example arising in the study of a mixed system, consisting of a first-order implicit differential equation and a differential inclusion, is given.…”
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Positive Solutions for the Initial Value Problem of Fractional Evolution Equations by He Yang, Yue Liang

“…As an example, we study the partial differential equation of the parabolic type of fractional order.…”
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Existence and Nonexistence of Positive Solutions for Fractional Three-Point Boundary Value Problems with a Parameter by Yunhong Li, Weihua Jiang

“…In this work, we investigate the existence and nonexistence of positive solutions for p-Laplacian fractional differential equation with a parameter. On the basis of the properties of Green’s function and Guo-Krasnosel’skii fixed point theorem on cones, the existence and nonexistence of positive solutions are obtained for the boundary value problems. …”
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Analytic Solutions of 2D Cubic Quintic Complex Ginzburg-Landau Equation by F. Waffo Tchuimmo, J. B. Gonpe Tafo, A. Chamgoue, N. C. Tsague Mezamo, F. Kenmogne, L. Nana

“…The particularity of these phase portraits obtained for new ordinary differential equation is the existence of homoclinic or heteroclinic orbits depending on the nature of equilibrium points. …”
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Uniqueness and radial symmetry for an inverse elliptic equation by B. Emamizadeh, M. H. Mehrabi

“…We consider an inverse rearrangement semilinear partial differential equation in a 2-dimensional ball and show that it has a unique maximizing energy solution. …”
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Bounds of Solutions of Integrodifferential Equations by Zdeněk Šmarda

“…Some new integral inequalities are given, and bounds of solutions of the following integro-differential equation are determined: x'(t)-F(t,x(t),∫0tk(t,s,x(t),x(s))ds)=h(t), x(0)=x0, where h:R+→R, k:R+2×R2→R, F:R+×R2→R are continuous functions, R+=[0,∞).…”
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An oriented coincidence index for nonlinear Fredholm inclusions with nonconvex-valued perturbations

“…An example arising in the study of a mixed system, consisting of a first-order implicit differential equation and a differential inclusion, is given.…”
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Qualitatively Stable Nonstandard Finite Difference Scheme for Numerical Solution of the Nonlinear Black–Scholes Equation by Mohammad Mehdizadeh Khalsaraei, Ali Shokri, Zahra Mohammadnia, Hamid Mohammad Sedighi

“…In this paper, we use a numerical method for solving the nonlinear Black–Scholes partial differential equation of the European option under transaction costs, which is based on the nonstandard discretization of the spatial derivatives. …”
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The Numerical Solution of the Bitsadze-Samarskii Nonlocal Boundary Value Problems with the Dirichlet-Neumann Condition by Allaberen Ashyralyev, Elif Ozturk

“…A procedure of modified Gauss elimination method is used for solving these difference schemes for the two-dimensional elliptic differential equation. The method is illustrated by numerical examples.…”
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