Delta-Nabla Type Maximum Principles for Second-Order Dynamic Equations on Time Scales and Applications by Jiang Zhu, Dongmei Liu

“…By using these maximum principles, the uniqueness theorems of the solutions, the approximation theorems of the solutions, the existence theorem, and construction techniques of the lower and upper solutions for second-order linear and nonlinear initial value problems and boundary value problems on time scales are proved, the oscillation of second-order mixed delat-nabla differential equations is discussed and, some maximum principles for second order mixed forward and backward difference dynamic system are proved.…”
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Positive Solutions for BVP of Fractional Differential Equation with Integral Boundary Conditions by Min Li, Jian-Ping Sun, Ya-Hong Zhao

“…In this paper, we consider a class of boundary value problems of nonlinear fractional differential equation with integral boundary conditions. …”
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Existence of Positive Solutions of a Discrete Elastic Beam Equation by Ruyun Ma, Jiemei Li, Chenghua Gao

“…We consider the existence of positive solutions of the nonlinear boundary value problems of fourth-order difference equations Δ4u(t−2)−ra(t)f(u(t))=0, t∈T2, u(1)=u(T+1)=Δ2u(0)=Δ2u(T)=0, where r is a constant, a:T2→(0,∞),  and  f:[0,∞)→[0,∞) is continuous. …”
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Quantitative analysis and stability results in $ \beta $-normed space for sequential differential equations with variable coefficients involving two fractional derivatives by Debao Yan

“…This article conducted an analysis on quantitative properties and stability in a $ \beta $-normed space for a category of boundary value problems of nonlinear two-term fractional-order sequential differential equations with variable coefficients. …”
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Stability and optimization in structured population models on graphs by Rinaldo M. Colombo, Mauro Garavello

“…We prove existence and uniqueness of solutions, continuous dependence from the initial datum and stability with respect to the boundary condition in a class of initial--boundary value problems for systems of balance laws. The particular choice of the boundary condition allows to comprehend models with very different structures. …”
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Optimal Control of Mechanical Systems by Vadim Azhmyakov

“…Using the variational structure of the solution of the corresponding boundary-value problems, we reduce the initial optimal control problem to an auxiliary problem of multiobjective programming. …”
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Hydrodynamics of a Free Floating Vertical Axisymmetric Oscillating Water Column Device by S. A. Mavrakos, D. N. Konispoliatis

“…Three types of first-order boundary value problems are investigated in order to calculate the velocity potential of the flow field around the device. …”
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Solution of Second-Order IVP and BVP of Matrix Differential Models Using Matrix DTM by Reza Abazari, Adem Kılıcman

“…We introduce a matrix form of differential transformation method (DTM) and apply for nonlinear second-order initial value problems (IVPs) and boundary value problems (BVPs) of matrix models which are given by 𝐮(𝑡)=𝑓(𝑡,𝐮(𝑡),𝐮(𝑡)) and subject to initial conditions 𝐮(𝑎)=𝐮0,𝐮(𝑎)=𝐮1 and boundary conditions 𝐮(𝑎)=𝐮0,𝐮(𝑏)=𝐮1, where 𝐮0,𝐮1∈𝑅𝑟×𝑞. …”
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Connection Formulae between Ellipsoidal and Spherical Harmonics with Applications to Fluid Dynamics and Electromagnetic Scattering by Michael Doschoris, Panayiotis Vafeas

“…The environment of the ellipsoidal system, significantly more complex than the spherical one, provides the necessary settings for tackling boundary value problems in anisotropic space. However, the theory of Lamé functions and ellipsoidal harmonics affiliated with the ellipsoidal system is rather complicated. …”
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Semi-Fredholm Solvability in the Framework of Singular Solutions for the (3+1)-D Protter-Morawetz Problem by Nedyu Popivanov, Todor Popov, Allen Tesdall

“…For the four-dimensional nonhomogeneous wave equation boundary value problems that are multidimensional analogues of Darboux problems in the plane are studied. …”
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Analyzing Similarity Solution of Modified Fisher Equation by Esen Hanaç Duruk, Mehmet Emir Koksal, Ram Jiwari

“…Some initial-boundary value problems are considered test problems. The numerical results indicate extremely exact and stable initial and boundary conditions in the same domain with dissimilar time ranges.…”
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Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions by Mısır J. Mardanov, Yagub A. Sharifov, Kamala E. Ismayilova

“…Sufficient conditions are found for the existence and uniqueness of solutions for the boundary value problems for the first order nonlinear system of the impulsive ordinary differential equations with three-point boundary conditions. …”
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Computing the Electric and Magnetic Matrix Green’s Functions in a Rectangular Parallelepiped with a Perfect Conducting Boundary by V. G. Yakhno, Ş. Ersoy

“…This method is based on approximation (regularization) of the Dirac delta function and its derivatives, which appear in the differential equations for magnetic and electric Green’s functions, and the Fourier series expansion meta-approach for solving the elliptic boundary value problems. The elements of approximate Green’s functions are found explicitly in the form of the Fourier series with a finite number of terms. …”
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Tricomi problem and integral equations by N. B. Pleshchinskii

“…An explicit solution of the characteristic singular equation with a Cauchy kernel was obtained without involving the theory of boundary value problems for analytic functions.…”
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Analytic Approximation of Solutions of Parabolic Partial Differential Equations with Variable Coefficients by Vladislav V. Kravchenko, Josafath A. Otero, Sergii M. Torba

“…Their use allows one to obtain an explicit solution of the noncharacteristic Cauchy problem with sufficiently regular Cauchy data as well as to solve numerically initial boundary value problems. In the paper, the Dirichlet boundary conditions are considered; however, the proposed method can be easily extended onto other standard boundary conditions. …”
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On Motion Planning for Point-to-Point Maneuvers for a Class of Sailing Vehicles by Lin Xiao, Jerome Jouffroy

“…Starting from a simple dynamic model of sailing vessels in one dimension, this paper first considers their associated controllability issues, with the so-called no-sailing zone as a starting point, and it links them with a motion planning strategy using two-point boundary value problems as the main mathematical tool. This perspective is then expanded to do point-to-point maneuvers of sailing vehicles in the plane, that is, automatic path generation combined with computation of control input profiles. …”
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Stability analysis for first-order nonlinear differential equations with three-point boundary conditions by Kamala E. Ismayilova

“…Several theorems are proved concerning the existence and uniqueness of solutions to the boundary value problems for the first order nonlinear system of ordinary differential equations with three-point boundary conditions. …”
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Asymptotic and numerical solutions for diffusion models for compounded risk reserves with dividend payments by S. Shao, C. L. Chang

“…After defining the process of conditional probability in finite time, martingale theory turns the nonlinear stochastic differential equation to a special class of boundary value problems defined by a parabolic equation with a nonsmooth coefficient of the convection term. …”
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Constructive Existence of (1,1)-Solutions to Two-Point Value Problems for Fuzzy Linear Multiterm Fractional Differential Equations by HuiChol Choi, SungHyok Kwon, Kinam Sin, Sunae Pak, Sungryol So

“…In this paper, we consider the following two-point boundary value problems of fuzzy linear fractional differential equations: (Dc1,1αy)(t)⊕b(t)⊗(Dc1,1βy)(t)⊕c(t)⊗y(t)=f(t), t∈(0,1), y(0)=y0 and y(1)=y1, where b,c∈C(I), b(t),c(t)≥0, y,f∈C(I,RF), I=[0,1], y0,y1∈RF and 1<β<α≤2. …”
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Construction of Exact Parametric or Closed Form Solutions of Some Unsolvable Classes of Nonlinear ODEs (Abel's Nonlinear ODEs of the First Kind and Relative Degenerate Equations) by Dimitrios E. Panayotounakos, Theodoros I. Zarmpoutis

“…The nonlinear initial or boundary value problems are also investigated. Finally, introducing a relative mathematical methodology, we construct the exact parametric or closed form solutions for several degenerate Abel's equation of the first kind.…”
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