1,838 Results Found

In this paper, we study inverse nodal problems for a boundary value problem. A uniqueness result for the potential function and a reconstruction method are obtained. By using the nodal points as input data, we compute the approximation solution of th...

A nonlocal analogue of the biharmonic operator with involution-type transformations was considered. For the corresponding biharmonic equation with involution, we investigated the solvability of boundary value problems with a fractional-order boundary...

We provide a short introduction of new and well-known facts relating non-local operators and irregular domains. Cauchy problems and boundary value problems are considered in case non-local operators are involved. Such problems lead to anomalous behav...

Due to the restrictive growth and/or monotonicity requirements inherent in their employment, classical iterative fixed-point theorems are rarely used to approximate solutions to an integral operator with Green’s function kernel whose fixed poin...

We consider a non-standard nonlinear singularly perturbed 2D initial-boundary value problem with Venttsel type boundary conditions, arising in homogenization of radiative-conductive heat transfer problems. We establish existence, uniqueness and regul...

In this paper, we study the stationary boundary value problem derived from the magnetic (non) insulated regime on a plane diode. Our main goal is to prove the existence of non-negative solutions for that nonlinear singular system of second-order ordi...

This article is a review of ongoing research on analytical, numerical, and mixed methods for the solution of the third-order nonlinear Falkner–Skan boundary-value problem, which models the non-dimensional velocity distribution in the laminar boundary...

We studied one essentially nonlinear two–point boundary value problem for a system of fractional differential equations. An original parametrization technique and a dichotomy-type approach led to investigation of solutions of two “model”-type fractio...

An efficient method for determining an initial guess to an iterative solution to the boundary value problem y" + (k/x)y′ + δe^y = 0 solved subject to y′(0) = 0 and y(1) = 0 is proposed. This initial guess overcomes the instability that occurs at the b...

In engineering disciplines, many important problems are to be formed as boundary value problems (BVPs) that have conditions that are specified at the extremes. To handle such problems, the conventional shooting method that transforms BVPs into initia...

This paper provides conditions for the existence of a solution to the second-order nonlinear boundary value problem on the half-line of the form $\Delta \left(a\left(n\right)\Delta x\left(n\right)\right)=f(n+1,x(n+1),\Delta x(n+1)),n\in \mathbb{N}\cup \left\{0\right\},$ with $\alpha x\left(0\right)+\beta a\left(0\right)\Delta x\left(0\right)=0,x(\infty )=d,$ where $d,\alpha ,\beta \in \mathbb{R}$, ${\alpha }^2+{\beta }^2>0$. To a...

This article deals with a special case of the Sturm–Liouville boundary value problem (BVP), an eigenvalue problem characterized by the Sturm–Liouville differential operator with unknown spectra and the associated eigenfunctions. By examin...

In this current work, we apply the topological degree and fixed point theorems to investigate the existence, uniqueness, and multiplicity of solutions for a boundary value problem associated with a fractional-order difference equation. Moreover, we p...

In this article, some new Lyapunov-type inequalities for a class of fractional boundary value problems are established by use of the nonsymmetry property of Green’s function corresponding to appropriate boundary conditions.

This paper investigates boundary value problems for a class of elliptic equations exhibiting uniform and non-uniform degeneracy, including cases of non-monotonic degeneration. A key objective is to identify conditions on the coefficients under which...

The paper aims to study a discrete boundary value problem of the Kirchhoff type based on the critical point theory and the strong maximum principle. Compared to the existing literature, the existence and multiplicity of positive solutions to the prob...

In this work, we present a boundary value problem of hybrid functional differential inclusion with nonlocal condition. The boundary conditions of integral and infinite points will be deduced. The existence of solutions and its maximal and minimal wil...

In this article, the coupled Kundu equations are analyzed using the Fokas unified method on the half-line. We resolve a Riemann–Hilbert (RH) problem in order to illustrate the representation of the potential function in the coupled Kundu equati...

The boundary value problem, BVP, for the PDE heat equation is studied and explained in this article. The problem declaration comprises two intervals; the (0, T) is the first interval and labels the heating of the inside burning chamber, and the secon...

We investigate a generalization of the equation $curl\overrightarrow{w}=\overrightarrow{g}$ to an arbitrary number n of dimensions, which is based on the well-known Moisil–Teodorescu differential operator. Explicit solutions are derived for a particular problem in bounded domains of...

We introduce some research results on a type of third-order boundary value problem for positive iterative solutions. The existence of solutions to these problems was proved using the monotone iterative technique. As an examination of the proposed met...

This paper provides results on the sign of the Green function (and its partial derivatives) of an n-th order boundary value problem subject to a wide set of homogeneous two-point boundary conditions. The dependence of the absolute value of the Green...

Mathematical models of fracture physics and mechanics are boundary value problems for differential equations and systems of equations with a singularity. There are two classes of problems with a singularity: with coordinated and uncoordinated degener...

In this article, we present a nonlocal Neumann boundary value problems for separate sequential fractional symmetric Hahn integrodifference equation. The problem contains five fractional symmetric Hahn difference operators and one fractional symmetric...

The solvability issues of counterpart Holmgren’s boundary value problem with mixed conditions for a degenerate four-dimensional second-order Gellerstedt equation $H\left(u\right)\equiv y^m{z}^k{t}^l{u}_{xx}+x^n{z}^k{t}^l{u}_{yy}+x^n{y}^m{t}^l{u}_{zz}+x^n{y}^m{z}^k{u}_{tt}=0,$$m,n,k,l\equiv const>0,$...

We investigate the boundary value problem for steady-state magnetohydrodynamic (MHD) equations with inhomogeneous mixed boundary conditions for a velocity vector, given the tangential component of a magnetic field. The problem represents the flow of...

This article investigates the boundary value problem for an extended stationary system of Nernst–Planck–Poisson equations, corresponding to a mathematical model of the influence of changes in the equilibrium coefficient on the transport o...

This paper presents an alternative methodology for finding the solution of the boundary value problem (BVP) for the linear partial differential operator. We are particularly interested in the linear operator ${\oplus }^k$, where ${\oplus }^k={♡}^k{♢}^k$, ${♡}^k$ is the b...

The existence of solutions of nonlocal fractional symmetric Hahn integrodifference boundary value problem is studied. We propose a problem of five fractional symmetric Hahn difference operators and three fractional symmetric Hahn integrals of differe...

We consider a two-step numerical approach for solving parabolic initial boundary value problems in 3D simply connected smooth regions. The method uses the Laplace transform in time, reducing the problem to a set of independent stationary boundary val...

In this article, we propose a fourth-order non-self-adjoint system of singular boundary value problems (SBVPs), which arise in the theory of epitaxial growth by considering hte equation $\frac{1}{r^{\beta }}{\left\{r^{\beta }{\left[\frac{1}{r^{\beta }}{\left(r^{\beta }{\Theta }^{\prime }\right)}^{{}^{\prime }}\right]}^{\prime }\right\}}^{{}^{\&pri}}$...

In this article, a modified implicit hybrid method for solving the fractional Bagley-Torvik boundary (BTB) value problem is investigated. This approach is of a higher order. We study the convergence, zero stability, consistency, and region of absolut...

In this paper, a multipoint boundary value problem for systems of integro-differential equations with involution has been studied. To solve the studied problem, the parameterization method is used. Based on the parametrization method, the studied pro...

The authors investigate the existence of solutions to a class of boundary value problems for fractional q-difference equations in a Banach space that involves a q-derivative of the Caputo type and nonlinear integral boundary conditions. Their result...

We consider the periodic boundary value problem (PBVP) for a semilinear fractional-order delayed functional differential inclusion in a Banach space. We introduce and study a multivalued integral operator whose fixed points coincide with mild solutio...

This study utilizes approximation techniques to address a boundary value problem involving a differential equation with a delayed argument. The problem is approached through analytical techniques by transforming it firstly into an equivalent integral...

The Sturm–Liouville boundary value problem (SLBVP) stands as a fundamental cornerstone in the realm of mathematical analysis and physical modeling. Also known as the Sturm–Liouville problem (SLP), this paper explores the intricacies of th...

A nonlocal boundary value problem for a couple of two scalar nonlinear differential equations with several generalized proportional Caputo fractional derivatives and a delay is studied. The exact solution of the scalar nonlinear differential equation...

We construct the Green function of the first boundary-value problem for a diffusion-wave equation with fractional derivative with respect to the time variable. The Green function is sought in terms of a double-layer potential of the equation under co...

In this paper, the well-known Föppl–Hencky membrane problem—that is, the problem of axisymmetric deformation of a transversely uniformly loaded and peripherally fixed circular membrane—was resolved, and a more refined closed-fo...

In this paper, we study a backward problem for a fractional Rayleigh–Stokes equation by using a quasi-boundary value method. This problem is ill-posed; i.e., the solution (if it exists) does not depend continuously on the data. To overcome its...

In this paper, based on critical point theory, we mainly focus on the multiplicity of nontrivial solutions for a nonlinear discrete Dirichlet boundary value problem involving the mean curvature operator. Without imposing the symmetry or oscillating b...

This article presents a novel approach to looking at steady-state thermoelastic boundary value problems in isotropic elastic plates with curvilinear holes using a complex variable approach and rational conformal mappings. The physical domain with a n...

In this paper, we consider a boundary value problem for a nonlinear partial differential equation of mixed type with Hilfer operator of fractional integro-differentiation in a positive rectangular domain and with spectral parameter in a negative rect...

This article is to study a three-point boundary value problem of Hadamard fractional p-Laplacian differential equation. When our nonlinearity grows $(p-1)$ -superlinearly and $(p-1)$ -sublinearly, the existence of positive solutions...

This paper studies a class of integral boundary value problem of fractional q-difference equations. We first give an explicit expression for the associated Green’s function and obtain an important property of the function. The new property allo...

In this paper, we establish several necessary conditions to confirm the uniqueness-existence of solutions to an extended multi-order finite-term fractional differential equation with double-order integral boundary conditions with respect to asymmetri...

This article proposes various new approximate analytical solutions of the boundary value problem for the non-stationary system of Nernst–Planck–Poisson (NPP) equations in the diffusion layer of an ideally selective ion-exchange membrane a...

The goal of this work is to study a multi-term boundary value problem (BVP) for fractional differential equations in the variable exponent Lebesgue space ($L^{p(·)}$). Both the existence, uniqueness, and the stability in the sense of Ulam–Hye...

In this paper, we focus on the multiplicity of positive solutions for a singular tempered fractional initial-boundary value problem with a p-Laplacian operator and a changing-sign perturbation term. By introducing a truncation function and combing wi...