Homotopy Perturbation Method to Obtain Positive Solutions of Nonlinear Boundary Value Problems of Fractional Order by Hossein Jafari, Khadijeh Bagherian, Seithuti P. Moshokoa

“…We use the homotopy perturbation method for solving the fractional nonlinear two-point boundary value problem. The obtained results by the homotopy perturbation method are then compared with the Adomian decomposition method. …”
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Existence of Three Positive Solutions for m-Point Discrete Boundary Value Problems with p-Laplacian by Yanping Guo, Wenying Wei, Yuerong Chen

“…Using a new fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem.…”
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Spectral Criteria for Solvability of Boundary Value Problems and Positivity of Solutions of Time-Fractional Differential Equations by Valentin Keyantuo, Carlos Lizama, Mahamadi Warma

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Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory by Jing Chen, X. H. Tang

“…We study the existence and multiplicity of solutions for the following fractional boundary value problem: (𝑑/𝑑𝑡)((1/2)0𝐷𝑡−𝛽(𝑢′(𝑡))+(1/2)𝑡𝐷𝑇−𝛽(𝑢′(𝑡)))+∇𝐹(𝑡,𝑢(𝑡))=0,a.e.𝑡∈[0,𝑇],𝑢(0)=𝑢(𝑇)=0, where 𝐹(𝑡,⋅) are superquadratic, asymptotically quadratic, and subquadratic, respectively. …”
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Boundary Value Problem for Nonlinear Implicit Generalized Hilfer-Type Fractional Differential Equations with Impulses by Abdelkrim Salim, Mouffak Benchohra, Jamal Eddine Lazreg, Gaston N’Guérékata

“…This article deals with some existence, uniqueness, and Ulam-Hyers-Rassias stability results for a class of boundary value problem for nonlinear implicit fractional differential equations with impulses and generalized Hilfer Fractional derivative. …”
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Existence of Solutions for Fractional Integro-Differential Equation with Multipoint Boundary Value Problem in Banach Spaces by Yulin Zhao, Li Huang, Xuebin Wang, Xianyang Zhu

“…By means of the fixed-point theorem in the cone of strict-set-contraction operators, we consider the existence of a nonlinear multi-point boundary value problem of fractional integro-differential equation in a Banach space. …”
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Infinitely Many Solutions for a Generalized Periodic Boundary Value Problem without the Evenness Assumption by Xiaodong Gu, Mingliang Song

“…In this paper, we investigate infinitely many solutions for the generalized periodic boundary value problem −x″−B0tx+B1tx=λ∇xVt,xa.e.t∈0,1,x1=Mx0,x′1=Nx′0 under the potential function Vt,x without the evenness assumption and obtain two new existence results by the multiple critical point theorem. …”
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Global Structure of Positive Solutions for a Singular Fourth-Order Integral Boundary Value Problem by Wenguo Shen, Tao He

“…We consider fourth-order boundary value problems u′′′′(t)=λh(t)f(u(t)),  0<t<1,  u(0)=∫01‍u(s)dα(s),  u′(0)=u(1)=u′(1)=0, where ∫01‍u(s)dα(s) is a Stieltjes integral with α(t) being nondecreasing and α(t) being not a constant on [0,1]; h(t) may be singular at t=0 and t=1, h∈C((0,1),[0,∞)) with h(t)≢0 on any subinterval of (0,1); f∈C([0,∞),[0,∞)) and f(s)>0 for all s>0, and f0=∞,  f∞=0,  f0=lims→0+f(s)/s,  f∞=lims→+∞f(s)/s. …”
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Positive Solutions to Nonlinear Higher-Order Nonlocal Boundary Value Problems for Fractional Differential Equations by Mujeeb Ur Rehman, Rahmat Ali Khan

“…We use the classical tools from functional analysis to obtain sufficient conditions for the existence and uniqueness of positive solutions to the boundary value problems. We also obtain conditions for the nonexistence of positive solutions to the problem. …”
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On the existence of solution of a two-point boundary value problem in a cylindrical floating zone by Shi Yongdong, Du Liangsheng

“…Existence of one solution for a two-point boundary value problem with a positive parameter Q arising in the study of surface-tension-induced flows of a liquid metal or semiconductor is studied. …”
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Existence of a positive solution for an nth order boundary value problem for nonlinear difference equations by Susan D. Lauer, Johnny Henderson

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Existence of Positive Solutions for m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation by Moustafa El-Shahed, Wafa M. Shammakh

“…We investigate an m-point boundary value problem for nonlinear fractional differential equations. …”
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The Existence of Positive Solutions for Boundary Value Problem of the Fractional Sturm-Liouville Functional Differential Equation by Yanan Li, Shurong Sun, Zhenlai Han, Hongling Lu

“…We study boundary value problems for the following nonlinear fractional Sturm-Liouville functional differential equations involving the Caputo fractional derivative:   CDβ(p(t)CDαu(t)) + f(t,u(t-τ),u(t+θ))=0, t∈(0,1),  CDαu(0)= CDαu(1)=( CDαu(0))=0, au(t)-bu′(t)=η(t), t∈[-τ,0], cu(t)+du′(t)=ξ(t), t∈[1,1+θ], where   CDα,  CDβ denote the Caputo fractional derivatives, f is a nonnegative continuous functional defined on C([-τ,1+θ],ℝ), 1<α≤2, 2<β≤3, 0<τ, θ<1/4 are suitably small, a,b,c,d>0, and η∈C([-τ,0],[0,∞)), ξ∈C([1,1+θ],[0,∞)). …”
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A Subdivision Based Iterative Collocation Algorithm for Nonlinear Third-Order Boundary Value Problems by Syeda Tehmina Ejaz, Ghulam Mustafa

“…We construct an algorithm for the numerical solution of nonlinear third-order boundary value problems. This algorithm is based on eight-point binary subdivision scheme. …”
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Uniqueness and Existence of Positive Solutions for Singular Differential Systems with Coupled Integral Boundary Value Problems by Yujun Cui, Lishan Liu, Xingqiu Zhang

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Numerical Algorithm for the Third-Order Partial Differential Equation with Three-Point Boundary Value Problem by Jing Niu, Ping Li

“…A numerical method based on the reproducing kernel theorem is presented for the numerical solution of a three-point boundary value problem with an integral condition. Using the reproducing property and the existence of orthogonal basis in a new reproducing kernel Hilbert space, we obtain a representation of exact solution in series form and its approximate solution by truncating the series. …”
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On an Initial Boundary Value Problem for a Class of Odd Higher Order Pseudohyperbolic Integrodifferential Equations by Said Mesloub

“…This paper is devoted to the study of the well-posedness of an initial boundary value problem for an odd higher order nonlinear pseudohyperbolic integrodifferential partial differential equation. …”
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Multiple Solutions for Boundary Value Problems of th-Order Nonlinear Integrodifferential Equations in Banach Spaces by Yanlai Chen

“…The boundary value problems of a class of th-order nonlinear integrodifferential equations of mixed type in Banach space are considered, and the existence of three solutions is obtained by using the fixed-point index theory.…”
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New solvability condition of 2-d nonlocal boundary value problem for Poisson’s operator on rectangle by Dovlet M. Dovletov

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On a two-point boundary value problem for second-order differential inclusions on Riemannian manifolds by Yuri E. Gliklikh, Andrei V. Obukhovskii

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