Related papers: Regions of existence for a class of nonlinear diff…
The aim of this article is to prove the existence of solution and compute the region of existence for a class of 4-point BVPs defined as, \begin{eqnarray*} &&-u''(x)=\psi(x,u,u'), \quad 0<x<1, &&u'(0)=\lambda_{1}u(\xi), \quad…
Singular boundary value problems (SBVPs) arise in various fields of Mathematics, Engineering and Physics such as boundary layer theory, gas dynamics, nuclear physics, nonlinear optics, etc. The present monograph is devoted to systems of…
In this paper, we study the initial value problem for infinite dimensional fractional non-autonomous reaction-diffusion equations. Applying general time-splitting methods, we prove the existence of solutions globally defined in time using…
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 classical wave equation in the space of generalized functions (distributions)is considered. The Distributions Method of building the solutions of nonstationary boundary value problems (NBVP) for wave equations in coordinates spaces of…
Let $\Omega \subset \mathbb{R}^N$, $N \geq 2$, be a smooth bounded domain. For $s \in (1/2,1)$, we consider a problem of the form \[ \left\{\begin{aligned} (-\Delta)^s u & = \mu(x)\, \mathbb{D}_s^{2}(u) + \lambda f(x)\,, & \quad \mbox{in}…
We provide a new existence result for abstract nonlinear operator systems in normed spaces, by means of topological methods. The solution is located within the product of annular regions and conical shells. The theoretical result possesses…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…
The global existence and boundedness of solutions to volume-surface reaction diffusion systems with a mass control condition are investigated. Such systems arise typically in e.g. cell biology, ecology or fluid mechanics, when some…
We establish several bounds for solutions to elliptic/parabolic cross-diffusion systems of $m$ equations ($m\ge2$) on 2d/3d domains $\Og$. We settle the existence and global existence problems in these cases and also provide new…
The purpose of the present work is to study the existence of solutions to initial value problems for nonlinear first order differential systems with nonlinear nonlocal boundary conditions of functional type. The existence results are…
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…
In this paper, we deal with analysis of the initial-boundary value problems for the semilinear time-fractional diffusion equations, while the case of the linear equations was considered in the first part of the present work. These equations…
This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their…
The quasi-variational inequalities play a significant role in analyzing a wide range of real-world problems. However, these problems are more complicated to solve than variational inequalities as the constraint set is based on the current…
Non-local advection is a key process in a range of biological systems, from cells within individuals to the movement of whole organisms. Consequently, in recent years, there has been increasing attention on modelling non-local advection…
This paper is devoted to prove the existence of one or multiple solutions of a wide range of nonlinear differential boundary value problems. To this end, we obtain some new fixed point theorems for a class of integral operators. We follow…
In this work, we study the global existence of solutions for a class of semilinear nonlocal reaction-diffusion systems with $m$ components on a bounded domain $\Omega$ in $\mathbb{R}^n$ with smooth boundary. The initial data is assumed to…
In this paper, we consider a class of nonlinear fractional differential equations involving Hilfer derivative with boundary conditions. First, we obtain an equivalent integral for the given boundary value problem in weighted space of…