A Generalized Nonlinear Gronwall-Bellman Inequality with Maxima in Two Variables by Yong Yan

“…We apply our result to a boundary value problem of a partial differential equation with maxima for uniqueness.…”
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Multiple Positive Solutions for Nonlinear Semipositone Fractional Differential Equations by Wen-Xue Zhou, Ji-Gen Peng, Yan-Dong Chu

“…We present some new multiplicity of positive solutions results for nonlinear semipositone fractional boundary value problem D0+αu(t)=p(t)f(t,u(t))-q(t),0<t<1,u(0)=u(1)=u'(1)=0, where 2<α≤3 is a real number and D0+α is the standard Riemann-Liouville differentiation. …”
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Asymptotic behaviour of solutions for porous medium equation with periodic absorption by Yin Jingxue, Wang Yifu

“…We are interested in the discussion of asymptotic behaviour of solutions of the first boundary value problem for the equation. In contrast to the equation without sources, we show that the solutions may not decay but may be attracted into any small neighborhood of the set of all nontrivial periodic solutions, as time tends to infinity. …”
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Positive Solutions for Nonlinear Singular Differential Systems Involving Parameter on the Half-Line by Lishan Liu, Ying Wang, Xinan Hao, Yonghong Wu

“…By using the upper-lower solutions method and the fixed-point theorem on cone in a special space, we study the singular boundary value problem for systems of nonlinear second-order differential equations involving two parameters on the half-line. …”
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On the Modified Jump Problem for the Laplace Equation in the Exterior of Cracks in a Plane by P. A. Krutitskii, A. Sasamoto

“…The boundary value problem for the Laplace equation outside several cracks in a plane is studied. …”
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Solving the Linear 1D Thermoelasticity Equations with Pure Delay by Denys Ya. Khusainov, Michael Pokojovy

“…For an initial-boundary value problem associated with this system, we prove a well-posedness result in a certain topology under appropriate regularity conditions on the data. …”
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A New Algorithm for System of Integral Equations by Abdujabar Rasulov, Adem Kilicman, Zainidin Eshkuvatov, Gulnora Raimova

“…Using the new algorithm it is also possible to solve an initial boundary value problem for system of parabolic equations. …”
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Computation of traveling wave fronts for a nonlinear diffusion-advection model by M. B. A. Mansour

“…Thesecond method is to construct time-dependent solutions bysolving an initial-moving boundary-value problem for the PDE system,showing another approximation for such wave solutions.…”
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Integrodifferential Equations of the Vector Problem of Electromagnetic Wave Diffraction by a System of Nonintersecting Screens and Inhomogeneous Bodies by Y. G. Smirnov, A. A. Tsupak

“…The original boundary value problem for Maxwell’s equations system is reduced to a system of integrodifferential equations in the regions occupied by the bodies and on the screen surfaces. …”
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Global Mild Solutions and Attractors for Stochastic Viscous Cahn-Hilliard Equation by Xuewei Ju, Hongli Wang, Desheng Li, Jinqiao Duan

“…This paper is devoted to the study of mild solutions for the initial and boundary value problem of stochastic viscous Cahn-Hilliard equation driven by white noise. …”
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Existence and Uniqueness Results for Hadamard-Type Fractional Differential Equations with Nonlocal Fractional Integral Boundary Conditions by Phollakrit Thiramanus, Sotiris K. Ntouyas, Jessada Tariboon

“…We study the existence and uniqueness of solutions for a fractional boundary value problem involving Hadamard-type fractional differential equations and nonlocal fractional integral boundary conditions. …”
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On More General Fractional Differential Equations Involving Mixed Generalized Derivatives with Nonlocal Multipoint and Generalized Fractional Integral Boundary Conditions by Wafa Shammakh, Hadeel Z. Alzumi, Bushra A. AlQahtani

“…This paper deals with the existence of solutions for a new boundary value problem involving mixed generalized fractional derivatives of Riemann-Liouville and Caputo supplemented with nonlocal multipoint boundary conditions. …”
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On the Multiplicity of Solutions for the Discrete Boundary Problem Involving the Singular ϕ-Laplacian by Zihua Qiu

“…In this paper, we consider the multiplicity of solutions for a discrete boundary value problem involving the singular ϕ-Laplacian. …”
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An Existence and Uniqueness Result for a Bending Beam Equation without Growth Restriction by Yongxiang Li, He Yang

“…We discuss the solvability of the fourth-order boundary value problem u(4)=f(t,u,u′′), 0≤t≤1, u(0)=u(1)=u′′(0)=u′′(1)=0, which models a statically bending elastic beam whose two ends are simply supported, where f:[0,1]×R2→R is continuous. …”
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Study of Hybrid Problems under Exponential Type Fractional-Order Derivatives by Mohammed S. Abdo, Sahar Ahmed Idris, M. Daher Albalwi, Tomadir Ahmed Idris

“…In this investigation, we develop a theory for the hybrid boundary value problem for fractional differential equations subject to three-point boundary conditions, including the antiperiodic hybrid boundary condition. …”
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Elastic Equilibrium of Porous Cosserat Media with Double Porosity by Roman Janjgava

“…A concrete boundary value problem for a concentric ring is solved.…”
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Solutions for m-Point BVP with Sign Changing Nonlinearity by Hua Su

“…We study the existence of positive solutions for the following nonlinear m-point boundary value problem for an increasing homeomorphism and homomorphism with sign changing nonlinearity: {(ϕ(u′(t)))′+a(t)f(t,u(t))=0, 0<t<1, u′(0)=∑i=1m−2aiu′(ξi), u(1)=∑i=1kbiu(ξi)−∑i=k+1sbiu(ξi)−∑i=s+1m−2biu′(ξi), where ϕ:R→R is an increasing homeomorphism and homomorphism and ϕ(0)=0. …”
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On the Lauwerier formulation of the temperature field problem in oil strata by Lyubomir Boyadjiev, Ognian Kamenov, Shyam Kalla

“…The paper is concerned with the fractional extension of the Lauwerier formulation of the problem related to the temperature field description in a porous medium (sandstone) saturated with oil (strata). The boundary value problem for the fractional heat equation is solved by means of the Caputo differintegration operator D∗(α) of order 0<α≤1 and the Laplace transform. …”
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Orthogonal Methods for Multilayer Structures in Heat Conduction Problems by V. A. Kudinov, E. V. Kotova, A. V. Eremin, A. E. Kuznetsova

“…Theoretical properties of a method for construction of analytical solutions pertaining to heat conduction boundary value problem for multilayer structures have been given on the basis of the Kantarovich orthogonal method.Methodology for construction of coordinate function systems has been developed that satisfy  boundary conditions in  any approximation and satisfy matching conditions at any number of contacting bodies. …”
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On Solutions to a Class of Functional Differential Equations with Time-Dependent Coefficients by Muhammad Mohsin, Syed Touqeer H. Shah, Ali A. Zaidi

“…In this paper, we study initial boundary value problems that involve functional (nonlocal) partial differential equations with variable coefficients. …”
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