Approximate Series Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology by Randhir Singh, Jitendra Kumar, Gnaneshwar Nelakanti

“…We introduce an efficient recursive scheme based on Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems. This approach is based on a modification of the ADM; here we use all the boundary conditions to derive an integral equation before establishing the recursive scheme for the solution components. …”
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On the Riesz Basisness of Systems Composed of Root Functions of Periodic Boundary Value Problems by Alp Arslan Kıraç

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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. …”
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Existence of Solutions for Sturm-Liouville Boundary Value Problem of Impulsive Differential Equations by Hong-Rui Sun, Ya-Ning Li, Juan J. Nieto, Qing Tang

“…This paper is concerned with the existence of solutions for Sturm-Liouville boundary value problem of a class of second-order impulsive differential equations, under different assumptions on the nonlinearity and impulsive functions, existence criteria of single and multiple solutions are established. …”
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Variational Iteration Method for Initial and Boundary Value Problems Using He's Polynomials by Syed Tauseef Mohyud-Din, Ahmet Yildirim, M. M. Hosseini

“…This paper outlines a detailed study of the coupling of He's polynomials with correction functional of variational iteration method (VIM) for solving various initial and boundary value problems. The elegant coupling gives rise to the modified versions of VIM which is very efficient in solving nonlinear problems of diversified nature. …”
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Monotone Iterative Solutions for Nonlinear Boundary Value Problems of Fractional Differential Equation by Chaozhu Hu, Bin Liu, Songfa Xie

“…By means of the method of quasi-lower and quasi-upper solutions and monotone iterative technique, we consider the nonlinear boundary value problems with Caputo fractional derivative and introduce two well-defined monotone sequences of quasi-lower and quasi-upper solutions which converge uniformly to the actual solution of the problem, and then the existence results of the solution for the problems are established. …”
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Positive Solutions for a System of Semipositone Fractional Difference Boundary Value Problems by Cheng Chen, Jiafa Xu, Donal O’Regan, Zhengqing Fu

“…Using the fixed point index, we establish two existence theorems for positive solutions to a system of semipositone fractional difference boundary value problems. We adopt nonnegative concave functions and nonnegative matrices to characterize the coupling behavior of our nonlinear terms.…”
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Numerical Solution of Two-Point Boundary Value Problems by Interpolating Subdivision Schemes by Ghulam Mustafa, Syeda Tehmina Ejaz

“…A numerical interpolating algorithm of collocation is formulated, based on 8-point binary interpolating subdivision schemes for the generation of curves, to solve the two-point third order boundary value problems. It is observed that the algorithm produces smooth continuous solutions of the problems. …”
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Lyapunov-Type Inequalities for Second-Order Boundary Value Problems with a Parameter by Haidong Liu

“…In this paper, we will establish some new Lyapunov-type inequalities for a class of second-order boundary value problems with a parameter. The inequalities generalize some early results in the literature.…”
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Rational hybrid block method for solving Bratu-type boundary value problems by S.S. Motsa, S.D. Oloniiju, H. Sithole-Mthethwa

“…This study introduces a novel rational hybrid block method for solving Bratu-type boundary value problems, offering significant improvements in efficiency and accuracy. …”
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Infinitely Many Positive Solutions for a Coupled Discrete Boundary Value Problem by Liuming Li, Zhan Zhou

“…In this paper, we obtain some results for the existence of infinitely many positive solutions for a coupled discrete boundary value problem. The approach is based on variational methods.…”
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Nontrivial Solutions of a Fully Fourth-Order Periodic Boundary Value Problem by Haitong Li, Minghe Pei, Libo Wang

“…We investigate the solvability of a fully fourth-order periodic boundary value problem of the form x(4)=f(t,x,x′,x′′,x′′′),  x(i)(0)=x(i)(T),      i=0,1,2,3, where f:[0,T]×R4→R satisfies Carathéodory conditions. …”
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Positive Solutions of a Fractional Boundary Value Problem with Changing Sign Nonlinearity by Yongqing Wang, Lishan Liu, Yonghong Wu

“…We discuss the existence of positive solutions of a boundary value problem of nonlinear fractional differential equation with changing sign nonlinearity. …”
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The Approximate Solution of Some Plane Boundary Value Problems of the Moment Theory of Elasticity by Roman Janjgava

“…Supposedly, the proposed method makes it possible to construct approximate solutions of quite a wide class of boundary value problems.…”
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['AN ENHANCED WAVELET BASED METHOD FOR NUMERICAL SOLUTION OF HIGH ORDER BOUNDARY VALUE PROBLEMS'] by Sirajul Haq, Muhammad Sohaib

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Fourth-Order Four-Point Boundary Value Problem: A Solutions Funnel Approach by Panos K. Palamides, Alex P. Palamides

“…We investigate the existence of positive or a negative solution of several classes of four-point boundary-value problems for fourth-order ordinary differential equations. …”
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On Third Order Stable Difference Scheme for Hyperbolic Multipoint Nonlocal Boundary Value Problem by Ozgur Yildirim, Meltem Uzun

“…This paper presents a third order of accuracy stable difference scheme for the approximate solution of multipoint nonlocal boundary value problem of the hyperbolic type in a Hilbert space with self-adjoint positive definite operator. …”
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Exact Number of Positive Solutions for a Class of Two-Point Boundary Value Problems by Yanmin Niu, Baoqiang Yan

“…This paper considers the existence of positive solutions of the boundary value problems and , where and is a positive parameter. …”
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Existence and Uniqueness of Solution to Nonlinear Boundary Value Problems with Sign-Changing Green’s Function by Peiguo Zhang, Lishan Liu, Yonghong Wu

“…By using the cone theory and the Banach contraction mapping principle, the existence and uniqueness results are established for nonlinear higher-order differential equation boundary value problems with sign-changing Green’s function. …”
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Some Properties of Solutions to Multiterm Fractional Boundary Value Problems with p-Laplacian Operator by KumSong Jong, HuiChol Choi, KyongJun Jang, SongGuk Jong, KyongSon Jon, Ok Ri

“…In this paper, we study some properties of positive solutions to a class of multipoint boundary value problems for nonlinear multiterm fractional differential equations with p-Laplacian operator. …”
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