On the spectrum of the negative Laplacian for general doubly-connected bounded domains by E. M. E. Zayed, A. I. Younis

“…Moreover, asymptotic expressions for the difference of eigenvalues related to impedance boundary value problems with different impedances are derived. …”
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A mathematical analysis of thermal explosions by Kazuaki Taira

“…This paper is devoted to the study of semilinear degenerate elliptic boundary value problems arising in combustion theory which obey the simple Arrhenius rate law and a general Newton law of heat exchange. …”
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The dirichlet boundary conditions and related natural boundary conditions in strengthened sobolev spaces for discretized parabolic problems by E. D'Yakonov

“…Correctness of initial boundary value problems and their discretizations are analyzed under unusual second-order boundary conditions, which can be considered as natural boundary conditions in strengthened Sobolev spaces and as improvements (in some cases) of the classical Dirichlet boundary conditions. …”
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Global Structure of Positive Solutions of a Discrete Problem with Sign-Changing Weight by Ruyun Ma, Chenghua Gao, Xiaoling Han, Xiaoqiang Chen

“…We are concerned with the global structure of positive solutions set of the discrete second-order boundary value problems Δ2u(t-1)+rm(t)f(u(t))=0,  t∈T,  u(0)=u(T+1)=0, where r∈ℝ is a parameter, m:T→ℝ changes its sign and m(t)≠0 for  t∈T.…”
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A Note on Fractional Equations of Volterra Type with Nonlocal Boundary Condition by Zhenhai Liu, Rui Wang

“…We deal with nonlocal boundary value problems of fractional equations of Volterra type involving Riemann-Liouville derivative. …”
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Approximate Solutions of Singular Two-Point BVPs Using Legendre Operational Matrix of Differentiation by A. Sami Bataineh, A. K. Alomari, I. Hashim

“…Exact and approximate analytical solutions of linear and nonlinear singular two-point boundary value problems (BVPs) are obtained for the first time by the Legendre operational matrix of differentiation. …”
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Generalized Green's functions for higher order boundary value matrix differential systems by R. J. Villanueva, L. Jodar

“…By using the concept of rectangular co-solution of certain algebraic matrix equation associated to the problem, an existence condition as well as an explicit closed form expression for the solution of possibly not well-posed boundary value problems is given avoiding the increase of the problem dimension.…”
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Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics by Tatiana Odzijewicz, Agnieszka B. Malinowska, Delfim F. M. Torres

“…We obtain necessary optimality conditions for the basic and isoperimetric problems, as well as natural boundary conditions for free-boundary value problems. The fractional action-like variational approach (FALVA) is extended and some applications to physics discussed.…”
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Existence Results for a Class of p-Laplacian Fractional Differential Equations with Integral Boundary Conditions by SunAe Pak, KumSong Jong, KyuNam O, HuiChol Choi

“…In this paper, we investigate the existence and uniqueness of solutions for a class of integral boundary value problems of nonlinear fractional differential equations with p-Laplacian operator. …”
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Quantum Difference Langevin System with Nonlocal q-Derivative Conditions by Surang Sitho, Sorasak Laoprasittichok, Sotiris K. Ntouyas, Jessada Tariboon

“…We introduce a new class of boundary value problems for Langevin quantum difference systems. …”
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Maximum Principle in the Optimal Control Problems for Systems with Integral Boundary Conditions and Its Extension by A. R. Safari, M. F. Mekhtiyev, Y. A. Sharifov

“…The sufficient condition is established for existence and uniqueness of the solution for a class of integral boundary value problems for fixed admissible controls. First-order necessary condition for optimality is obtained in the traditional form of the maximum principle. …”
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Approximation of the Fixed Point of Multivalued Quasi-Nonexpansive Mappings via a Faster Iterative Process with Applications by Godwin Amechi Okeke, Mujahid Abbas, Manuel de la Sen

“…In this paper, we approximate the fixed points of multivalued quasi-nonexpansive mappings via a faster iterative process and propose a faster fixed-point iterative method for finding the solution of two-point boundary value problems. We prove analytically and with series of numerical experiments that the Picard–Ishikawa hybrid iterative process has the same rate of convergence as the CR iterative process.…”
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The generalized Conley index and multiple solutions of semilinear elliptic problems by E. N. Dancer, Yihong Du

“…We establish some framework so that the generalized Conley index can be easily used to study the multiple solution problem of semilinear elliptic boundary value problems. Both the parabolic flow and the gradient flow are used. …”
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Existence of Solutions for Anti-Periodic Fractional Differential Inclusions with ψ-Caupto Fractional Derivative by Dandan Yang, Chuanzhi Bai

“…In this paper, we investigate the existence of solutions for a class of fractional boundary value problems with anti-periodic boundary value conditions with ψ-Caupto fractional derivative. …”
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On the Nusselt Solution of a Nonisothermal Two-Fluid Inclined Film Flow by Jürgen Socolowsky

“…The corresponding mathematical models often represent two-dimensional free boundary value problems for the Navier-Stokes equations or their modifications. …”
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Biharmonic eigen-value problems and Lp estimates by Chaitan P. Gupta, Ying C. Kwong

“…This paper is concerned mainly with the existence of and Lp-estimates for the solutions of certain biharmonic boundary value problems which are related to the first eigen-values of the associated biharmonic operators. …”
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The Use of Cubic Splines in the Numerical Solution of Fractional Differential Equations by W. K. Zahra, S. M. Elkholy

“…Therefore, cubic polynomial spline-function-based method combined with shooting method is considered to find approximate solution for a class of fractional boundary value problems (FBVPs). Convergence analysis of the method is considered. …”
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Rigorous 2D Model for Study of Pulsed and Monochromatic Waves Propagation Near the Earth’s Surface by Seil S. Sautbekov, Yuriy K. Sirenko, Nataliya P. Yashina, Aleksey A. Vertiy

“…This approach reduces the original open initial boundary value problems to the equivalent closed problems which can be solved numerically using the standard grid methods.…”
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Hyperbolic differential-operator equations on a whole axis by Yakov Yakubov

“…We give an abstract interpretation of initial boundary value problems for hyperbolic equations such that a part of initial boundary value conditions contains also a differentiation on the time t of the same order as equations. …”
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Positive Solutions for a Weakly Singular Hadamard-Type Fractional Differential Equation with Changing-Sign Nonlinearity by Xinguang Zhang, Lixin Yu, Jiqiang Jiang, Yonghong Wu, Yujun Cui

“…In this paper, we focus on the existence of positive solutions for a class of weakly singular Hadamard-type fractional mixed periodic boundary value problems with a changing-sign singular perturbation. …”
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