Related papers: Nonlocal and multipoint boundary value problems fo…
We develop methods for the solution of inhomogeneous Robin type boundary value problems (BVPs) that arise for certain linear parabolic Partial Differential Equations (PDEs) on a half line, as well as a second order generalisation. We are…
In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multi-point second-order boundary value problem, with a fully differential equation. The noninvertibility of the linear part is overcome by a…
The problem of solving partial differential equations (PDEs) on manifolds can be considered to be one of the most general problem formulations encountered in computational multi-physics. The required covariant forms of balance laws as well…
This study investigates Dirichlet boundary condition related to a class of nonlinear parabolic problem with nonnegative $L^1$-data, which has a variable-order fractional $p$-Laplacian operator. The existence and uniqueness of renormalized…
We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…
Nonlinear two-point boundary value problems arise in numerous areas of application. The existence and number of solutions for various cases has been studied from a theoretical standpoint. These results generally rely upon growth conditions…
We investigate the existence of positive solutions to the nonlinear second-order three-point integral boundary value problem \label{eq-1} {u^{\prime \prime}}(t)+a(t)f(u(t))=0,\ 0<t<T, u(0)={\beta}u(\eta),\…
The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…
We investigate the existence of positive solutions to the nonlinear second-order three-point integral boundary value problem \begin{equation*} \label{eq-1} \begin{gathered} {u^{\prime \prime}}(t)+f(t, u(t))=0,\ 0<t<T, \\…
A method for solving linear initial boundary value problems was recently reimplemented as a true spectral transform method. As part of this reformulation, the precise sense in which the spectral transforms diagonalize the underlying spatial…
In this paper, by using Krasnoselskii's fixed point theorem in a cone, we study the existence of single and multiple positive solutions to the three-point integral boundary value problem (BVP) \begin{equation*} \label{eq-1} \begin{gathered}…
In this work we propose a novel approach to investigate boundary value problems (BVPs) for fully third order differential equations. It is based on the reduction of BVPs to operator equations for the nonlinear terms but not for the…
This work investigates a class of moving boundary problems related to a nonlinear evolution equation featuring an exponential source term. We establish a connection to Stefan-type problems, for different boundary conditions at the fixed…
A non-classical initial and boundary value problem for a non-homogeneous one-dimensional heat equation for a semi-infinite material with a zero temperature boundary condition at the face $x=0$ is studied with the aim of finding explicit…
In this contribution, a stochastic nonlinear evolution system under Neumann boundary conditions is investigated. Precisely, we are interested in finding an existence and uniqueness result for a random heat equation coupled with a…
Aim of the paper is the qualitative analysis of a quasi-linear parabolic third order equation, which describes the evolution in a large class of dissipative models. As examples of some typical boundary problems, both Dirichlet's and…
We introduce and analyse a continuum model for an interacting particle system of Vicsek type. The model is given by a non-linear kinetic partial differential equation (PDE) describing the time-evolution of the density $f_t$, in the single…
This paper aims to investigate the existence and uniqueness of solutions for a sixth order differential equation involving nonlocal and integral boundary conditions. Firstly, we obtain the properties of the relevant Green's functions. The…
The focus of this study is on exploring some qualitative properties of solutions to a class of semilinear elliptic problems in bounded domains, where the boundary conditions depend non-locally on the unknown solution at specified interior…
Fractional differential equation (FDE) provides an accurate description of transport processes that exhibit anomalous diffusion but introduces new mathematical difficulties that have not been encountered in the context of integer-order…