Positive Solutions for Impulsive Differential Equations with Mixed Monotonicity and Optimal Control by Lingling Zhang, Noriaki Yamazaki, Rui Guo

“…Firstly, by using a fixed point theorem of mixed monotone operator, we study positive solutions of the boundary value problem for impulsive differential equations with mixed monotone terms, and sufficient conditions for existence and uniqueness of positive solutions will be established. …”
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Two Positive Solutions of Third-Order BVP with Integral Boundary Condition and Sign-Changing Green's Function by Bing-Wei Niu, Jian-Ping Sun, Qiu-Yan Ren

“…We are concerned with the following third-order boundary value problem with integral boundary condition:   u′′′(t)=f(t,u(t)),  t∈[0,1],  u′(0)=u(1)=0,  u′′(η)+∫αβ‍u(t)dt=0, where 1/2<α≤β≤1,  α+β≤4/3, and η∈(1/2,α]. …”
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A Mathematical Characterization for Patterns of a Keller-Segel Model with a Cubic Source Term by Shengmao Fu, Ji Liu

“…This paper deals with a Neumann boundary value problem for a Keller-Segel model with a cubic source term in a d-dimensional box (d=1,2,3), which describes the movement of cells in response to the presence of a chemical signal substance. …”
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A finite element method for a two-dimensional Pucci equation by Brenner, Susanne C., Sung, Li-yeng, Tan, Zhiyu

“…A nonlinear least-squares finite element method for strong solutions of the Dirichlet boundary value problem of a two-dimensional Pucci equation on convex polygonal domains is investigated in this paper. …”
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Application of Daftardar Jafari Method to First Grade MHD Squeezing Fluid Flow in a Porous Medium with Slip Boundary Condition by Inayat Ullah, M. T. Rahim, Hamid Khan

“…The governing equations are transformed to a single nonlinear boundary value problem. Daftardar Jafari Method (DJM) is used to solve the problem in order to obtain the velocity profile of the fluid. …”
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Binary mixture convection in a horizontal channel under the Soret effect action by Stepanova Irina

“…All possible statements of boundary value problems are studied in order to analyse thermal diffusion separation of binary mixture in a long horizontal channel with rigid walls. …”
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Multiple Positive Solutions of Third-Order BVP with Advanced Arguments and Stieltjes Integral Conditions by Jian Chang, Jian-Ping Sun, Ya-Hong Zhao

“…We consider the following third-order boundary value problem with advanced arguments and Stieltjes integral boundary conditions: u′′′t+ft,uαt=0,  t∈0,1,  u0=γuη1+λ1u and u′′0=0,  u1=βuη2+λ2u, where 0<η1<η2<1, 0≤γ,β≤1, α:[0,1]→[0,1] is continuous, α(t)≥t for t∈[0,1], and α(t)≤η2 for t∈[η1,η2]. …”
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Nonlinear eigenvalue problems in Sobolev spaces with variable exponent by Teodora-Liliana Dinu

“…We study the boundary value problem -div⁡((|∇u|p1(x)-2+|∇u|p2(x)-2)∇u)=f(x,u) in Ω, u=0 on ∂Ω, where Ω is a smooth bounded domain in ℝN. …”
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Mathematical Model of Pipeline Abandonment and Recovery in Deepwater by Xia-Guang Zeng, Meng-Lan Duan, Chen An

“…The mathematical model of pipeline abandonment and recovery is a moving boundary value problem, which means that it is hard to determine the length of the suspended pipeline segment. …”
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Shaping Single Offset Reflector Antennas Using Local Axis-Displaced Confocal Quadrics by Rafael A. Penchel, José R. Bergmann, Fernando J. S. Moreira

“…This work investigates a novel numerical procedure for the solution of an exact formulation for the Geometrical Optics synthesis of a single reflector antenna by simultaneously imposing Snell’s Law and Conservation of Energy in a tube of rays, yielding a second-order nonlinear partial differential equation of Monge-Ampère type, which can be solved as a boundary value problem. The investigation explores the interpolating properties of confocal quadrics to locally represent the shaped reflector surface. …”
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Existence Results for Fractional Difference Equations with Three-Point Fractional Sum Boundary Conditions by Thanin Sitthiwirattham, Jessada Tariboon, Sotiris K. Ntouyas

“…We consider a discrete fractional boundary value problem of the form Δαu(t)=f(t+α-1,u(t+α-1)),  t∈[0,T]ℕ0:={0,1,…,T},  u(α-2)=0,  u(α+T)=Δ-βu(η+β), where 1<α≤2, β>0, η∈[α-2,α+T-1]ℕα-2:={α-2,α-1,…,α+T-1}, and f:[α-1,α,…,α+T-1]ℕα-1×ℝ→ℝ is a continuous function. …”
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Some Qualitative Analyses of Neutral Functional Delay Differential Equation with Generalized Caputo Operator by Abdellatif Boutiara, Mohammed M. Matar, Mohammed K. A. Kaabar, Francisco Martínez, Sina Etemad, Shahram Rezapour

“…The existence and uniqueness results to the given boundary value problem are established with the help of the Dhage’s technique and Banach contraction principle. …”
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Effects of diffraction and radiation on a submerged sphere by Matiur Rahman

“…This type of problem is usually solved by using potential theory, and mathematically, we look for the solution of a velocity potential which satisfies Laplace's equation along with the free surface, body surface, and bottom boundary conditions in conjunction with a radiation condition. This boundary value problem, in fact, consists of two separate problems: (a) diffraction problem and (b) radiation problem.…”
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Fixed Point Results for α-ψ-Contractive Mappings Including Almost Contractions and Applications by Gonca Durmaz, Gülhan Mınak, Ishak Altun

“…Furthermore, we use our results to obtain the existence and uniqueness result for a solution of fourth order two-point boundary value problem.…”
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On Fixed Point of Quasi Contraction with Application to Integral Equation by Rhoda Chiroma, Shehu Shagari Mohammed, Jamilu Jiddah

“…As an application, one of our obtained corollaries is utilised to investigate new existence criteria for solving a class of boundary value problem.…”
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Analytical solution for the problem of pure bending of orthotropic micropolar plate by Damjan Jurković, Gordan Jelenić, Sara Grbčić Erdelj

“…When analysing the problem of pure bending of a plate, it can be noticed that, for cylindrical bending, a spatial problem collapses into a plane-strain problem. For such a boundary-value problem of the Cosserats' continuum, three engineering parameters are required: Young’s modulus, Poisson’s ratio and the characteristic length for bending. …”
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Finite and Infinte Time Blow Up of Solutions to Wave Equations with Combined Logarithmic and Power-Type Nonlinearities by Milena Dimova, Natalia Kolkovska, Nikolai Kutev

“…In this paper, we investigate the global behavior of the weak solutions to the initial boundary value problem for the nonlinear wave equation in a bounded domain. …”
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Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions by Bashir Ahmad, Juan J. Nieto

“…We study a Dirichlet boundary value problem for Langevin equation involving two fractional orders. …”
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Mixed Boundary-Value Analysis of Rocking Vibrations of an Elastic Strip Foundation on Elastic Soil with Saturated Substrata by Xiaohua Ma, Zhenyu Wang, Yuanqiang Cai, Changjie Xu

“…In this paper, we explore the mixed boundary-value problem of the rocking vibration of an elastic strip foundation on elastic soil with saturated substrata via Biot dynamic equations. …”
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First Characterization of a New Method for Numerically Solving the Dirichlet Problem of the Two-Dimensional Electrical Impedance Equation by Marco Pedro Ramirez-Tachiquin, Cesar Marco Antonio Robles Gonzalez, Rogelio Adrian Hernandez-Becerril, Ariana Guadalupe Bucio Ramirez

“…Based upon the elements of the modern pseudoanalytic function theory, we analyze a new method for numerically solving the forward Dirichlet boundary value problem corresponding to the two-dimensional electrical impedance equation. …”
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