Necessary and Sufficient Condition for the Existence of Solutions to a Discrete Second-Order Boundary Value Problem by Chenghua Gao

“…This paper is concerned with the existence of solutions for the discrete second-order boundary value problem Δ2u(t-1)+λ1u(t)+g(Δu(t))=f(t), t∈{1,2,…,T}, u(0)=u(T+1)=0, where T>1 is an integer, f:{1,…,T}→R, g:R→R is bounded and continuous, and λ1 is the first eigenvalue of the eigenvalue problem Δ2u(t-1)+λu(t)=0, t∈T, u(0)=u(T+1)=0.…”
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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

“…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. We also give some examples to illustrate the effectiveness of our main results.…”
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Positive Solutions for Three-Point Boundary Value Problem of Fractional Differential Equation with -Laplacian Operator by Shang-lin Yao, Guo-hui Wang, Zhi-ping Li, Li-jun Yu

“…We investigate the existence of multiple positive solutions for three-point boundary value problem of fractional differential equation with -Laplacian operator , where are the standard Riemann-Liouville derivatives with , and the constant is a positive number satisfying ; -Laplacian operator is defined as . …”
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Uniqueness and Asymptotic Behavior of Positive Solutions for a Fractional-Order Integral Boundary Value Problem by Min Jia, Xin Liu, Xuemai Gu

“…The existence, uniqueness, and asymptotic behavior of positive solutions to the singular nonlocal integral boundary value problem for fractional differential equation are obtained. …”
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Uniqueness and Multiplicity of Solutions for a Second-Order Discrete Boundary Value Problem with a Parameter by Xi-Lan Liu, Jian-Hua Wu

“…This paper is concerned with the existence of unique and multiple solutions to the boundary value problem of a second-order difference equation with a parameter, which is a complement of the work by J. …”
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Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value Problems by Hammad Khalil, Mohammed Al-Smadi, Khaled Moaddy, Rahmat Ali Khan, Ishak Hashim

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The Existence of Solutions for Four-Point Coupled Boundary Value Problems of Fractional Differential Equations at Resonance by Yumei Zou, Lishan Liu, Yujun Cui

“…A four-point coupled boundary value problem of fractional differential equations is studied. …”
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Triple Positive Solutions for Third-Order m-Point Boundary Value Problems on Time Scales by Jian Liu, Fuyi Xu

“…We study the following third-order m-point boundary value problems on time scales (φ(uΔ∇))∇+a(t)f(u(t))=0, t∈[0,T]T, u(0)=∑i=1m−2biu(ξi), uΔ(T)=0, φ(uΔ∇(0))=∑i=1m−2ciφ(uΔ∇(ξi)), where φ:R→R is an increasing homeomorphism and homomorphism and φ(0)=0, 0<ξ1<⋯<ξm−2<ρ(T). …”
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RETRACTED: Boundary value problems of degenerate integro-differential equations on the boundary of the region with application in filtration by Abdurazakov Abdujabbor, Fozilov Anvarjon, Makhmudova Nasiba, Mirzamakhmudova Nilufar

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Multiplicity of positive solutions for a third-order boundary value problem with nonlocal conditions of integral type by Sergey Smirnov

“…We prove the existence of multiple positive solutions for a nonlinear third-order nonlocal boundary value problem by applying Krasnosel’skii’s fixed point theorem. …”
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A boundary value problem with a discontinuous coefficient and containing a spectral parameter in the boundary condition by A. A. Darwish

Subjects: “…boundary value problems…”
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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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