Solutions of Second-Order m-Point Boundary Value Problems for Impulsive Dynamic Equations on Time Scales by Xue Xu, Yong Wang

“…We study a general second-order m-point boundary value problems for nonlinear singular impulsive dynamic equations on time scales uΔ∇(t)+a(t)uΔ(t)+b(t)u(t)+q(t)f(t,u(t))=0,t∈(0,1),t≠tk,uΔ(tk+)=uΔ(tk)-Ik(u(tk)), and k=1,2,…,n,u(ρ(0))=0,u(σ(1))=∑i=1m-2αiu(ηi)‍. …”
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Numerical Solutions for the Eighth-Order Initial and Boundary Value Problems Using the Second Kind Chebyshev Wavelets by Xiaoyong Xu, Fengying Zhou

“…A collocation method based on the second kind Chebyshev wavelets is proposed for the numerical solution of eighth-order two-point boundary value problems (BVPs) and initial value problems (IVPs) in ordinary differential equations. …”
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Periodic Boundary Value Problems for First-Order Impulsive Functional Integrodifferential Equations with Integral-Jump Conditions by Chatthai Thaiprayoon, Decha Samana, Jessada Tariboon

“…By developing a new comparison result and using the monotone iterative technique, we are able to obtain existence of minimal and maximal solutions of periodic boundary value problems for first-order impulsive functional integrodifferential equations with integral-jump conditions. …”
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Triple Positive Solutions of a Nonlocal Boundary Value Problem for Singular Differential Equations with p-Laplacian by Jufang Wang, Changlong Yu, Yanping Guo

“…We establish the existence of triple positive solutions of an m-point boundary value problem for the nonlinear singular second-order differential equations of mixed type with a p-Laplacian operator by Leggett-William fixed point theorem. …”
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Upper and Lower Solution Method for Fourth-Order Four-Point Boundary Value Problem on Time Scales by Ilkay Yaslan Karaca

“…We consider a fourth-order four-point boundary value problem for dynamic equations on time scales. …”
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Solvability for a nonlinear three-point boundary value problem with p-Laplacian-like operator at resonance by M. García-Huidobro, C. P. Gupta, R. Manásevich

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On real interpolation, finite differences, and estimates depending on a parameter for discretizations of elliptic boundary value problems by Davide Guidetti, Sergei Piskarev

“…Next, we apply them to estimate the resolvents of finite-difference discretizations of Dirichlet boundary value problems for elliptic equations in space dimensions one and two in analogs of spaces of continuous and Hölder continuous functions. …”
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Lyapunov-Type Inequalities for a Conformable Fractional Boundary Value Problem of Order 3<α≤4 by Imed Bachar, Hassan Eltayeb

“…We establish new Lyapunov-type inequalities for the following conformable fractional boundary value problem (BVP): Tαaut+q(t)u(t)=0,  a<t<b,  u(a)=u′(a)=u′′(a)=u′′(b)=0, where Tαa is the conformable fractional derivative of order α∈(3,4] and q is a real-valued continuous function. …”
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Numerical Treatment of Singularly Perturbed Two-Point Boundary Value Problems by Using Differential Transformation Method by Nurettin Doğan, Vedat Suat Ertürk, Ömer Akın

“…Differential transform method is adopted, for the first time, for solving linear singularly perturbed two-point boundary value problems. Four numerical examples are given to demonstrate the effectiveness of the present method. …”
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Positive Solutions for a System of Nonlinear Semipositone Boundary Value Problems with Riemann-Liouville Fractional Derivatives by Xiaowei Qiu, Jiafa Xu, Donal O’Regan, Yujun Cui

“…We study the existence of positive solutions for the system of nonlinear semipositone boundary value problems with Riemann-Liouville fractional derivatives D0+αD0+αu=f1t,u,u′,v,v′,  0<t<1, D0+αD0+αv=f2(t,u,u′,v,v′),  0<t<1, u0=u′0=u′(1)=D0+αu(0)=D0+α+1u(0)=D0+α+1u(1)=0, and v(0)=v′(0)=v′(1)=D0+αv(0)=D0+α+1v(0)=D0+α+1v(1)=0, where α∈(2,3] is a real number and D0+α is the standard Riemann-Liouville fractional derivative of order α. …”
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On the Solvability of a Resonant Third-Order Integral m-Point Boundary Value Problem on the Half-Line by O. F. Imaga, J. G. Oghonyon, P. O. Ogunniyi

“…In this work, the existence of at least one solution for the following third-order integral and m-point boundary value problem on the half-line at resonance ρtu′t″=wt,ut,u′t,u″t,t∈0,∞,u0=∑j=1m αj∫0ηj utdt,u′0=0,limt⟶∞ρtu′t′=0, will be investigated. …”
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A Quintic Spline-Based Computational Method for Solving Singularly Perturbed Periodic Boundary Value Problems by Puvaneswari Arumugam, Valanarasu Thynesh, Chandru Muthusamy, Higinio Ramos

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Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments by Zhaocai Hao, Yubo Huang

“…We discuss the existence of positive solutions to a class of fractional boundary value problem with changing sign nonlinearity and advanced arguments Dαx(t)+μh(t)f(x(a(t)))=0,t∈(0,1),2<α≤3,μ>0,x(0)=x′(0)=0,x(1)=βx(η)+λ[x],β>0, and  η∈(0,1), where Dα is the standard Riemann-Liouville derivative, f:[0,∞)→[0,∞) is continuous, f(0)>0, h :[0,1]→(−∞,+∞), and a(t) is the advanced argument. …”
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Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential Equation by Jinhua Wang, Hongjun Xiang, Yuling Zhao

“…We consider boundary value problem for nonlinear fractional differential equation D0+αu(t)+f(t,u(t))=0,  0<t<1,  n-1<α≤n,  n>3,  u(0)=u'(1)=u′′(0)=⋯=u(n-1)(0)=0, where D0+α denotes the Caputo fractional derivative. …”
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Flux Transport Characteristics of Free Boundary Value Problems for a Class of Generalized Convection-Diffusion Equation by Yunbin Xu, Meihua Wei

“…The similarity transformation is introduced for studying free boundary value problems for a class of generalized convection-diffusion equation. …”
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Boundary Value Problems for Systems of Second-Order Dynamic Equations on Time Scales with Δ-Carathéodory Functions by M. Frigon, H. Gilbert

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Initial Boundary Value Problem of the General Three-Component Camassa-Holm Shallow Water System on an Interval by Lixin Tian, Qingwen Yuan, Lizhen Wang

“…We study the initial boundary value problem of the general three-component Camassa-Holm shallow water system on an interval subject to inhomogeneous boundary conditions. …”
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A Chebyshev Spectral Method with Null Space Approach for Boundary-Value Problems of Euler-Bernoulli Beam by C. P. Hsu, C. F. Hung, J. Y. Liao

“…We proposed a Chebyshev spectral method with a null space approach for investigating the boundary-value problem of a nonprismatic Euler-Bernoulli beam with generalized boundary or interface conditions. …”
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Common Fixed-Point Theorems in the Partial b-Metric Spaces and an Application to the System of Boundary Value Problems by Muhammad Nazam, Zahida Hamid, Hamed Al Sulami, Aftab Hussain

“…As an application, we discuss the common solution to the system of boundary value problems.…”
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A necessary and sufficient condition for the existence of a unique solution of a discrete boundary value problem by Raghib Abu-Saris, Wajdi Ahmad

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