Related papers: Existence Result for Difference Equations on Non-U…
In this paper, we prove the existence of weak, veryweak and duality solutions to a class of elliptic problems involving singularity and measure data which is given by: $-\Delta u+(-\Delta)^s u = \frac{f(x)}{u^\gamma} +\mu$ in $\Omega$ with…
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…
Existence and spatio-temporal symmetric patterns of periodic solutions to second order reversible equivariant non-autonomous periodic systems with multiple delays are studied under the Hartman-Nagumo growth conditions. The method is based…
In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP) for the following second-order differential equation \begin{equation*} \begin{gathered} {u^{\prime \prime }}(t)+\lambda…
We derive some existence results for the solutions of the Tzitz\'eica equation \begin{equation*} -\Delta u + h_1(x)e^{Au} + h_2(x)e^{-Bu}=0 \end{equation*} and the generalized Tzitz\'eica equation \begin{equation*} -\Delta u +…
In this work, we consider a boundary value problem for nonlinear triharmonic equation. Due to the reduction of nonlinear boundary value problems to operator equation for nonlinear terms we establish the existence, uniqueness and positivity…
The work considers a system of fractional order partial differential equations. The existence and uniqueness theorems for the classical solution of initial-boundary value problems are proved in two cases: 1) the right-hand side of the…
In this paper, we study the existence of solutions for the following superlinear elliptic equation with nonlinear boundary value condition $$ \left\{ \begin{array}{ll} -\Delta u+u=|u|^{r-2}u &\text{in} \; \Omega,\\ \\ \frac{\partial…
This paper investigates the existence of solutions for a class of nonlinear higher-order dynamic equations subject to mixed boundary conditions. We consider boundary value problems in which the nonlinear reaction functions satisfy…
We study the Dirichlet problem of the following discrete infinity Laplace equation on unbounded subgraphs \begin{equation*} \Delta_{\infty}u(x):=\inf_{y\sim x}u(y)+\sup_{y\sim x}u(y)-2u(x)=f(x). \end{equation*} For the homogeneous case…
The approximate solution of the Cauchy problem for second-order evolution equations is performed, first of all, using three-level time approximations. Such approximations are easily constructed and relatively uncomplicated to investigate…
We introduce a fractional variant of the Cahn-Hilliard equation settled in a bounded domain and with a possibly singular potential. We first focus on the case of homogeneous Dirichlet boundary conditions, and show how to prove the existence…
This article focuses on a nonlinear Neumann boundary feedback control formulation for the viscous Burgers' equation and develops a class of finite difference schemes to achieve global stabilization. The proposed procedure, known as the…
We establish existence and uniqueness results for nonlinear elliptic Dirichlet boundary value problems on n-dimensional time scale domains. Time scales provide a unified framework that encompasses continuous, discrete, and hybrid settings.…
A new formulation of boundary value problems in gradient elasticity is presented in this work. The main outcome is the construction of partial differential systems of second order, which are typically equivalent with the well known fourth…
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 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…
This article establishes existence, non-existence and Liouville-type theorems for nonlinear equations of the form $$-div (|x|^{a} D u ) = f(x,u), ~ u > 0,\, \mbox{ in } \Omega,$$ where $N \geq 3$, $\Omega$ is an open domain in…
In this paper, we study the nonexistence of positive solutions for the following two mixed boundary value problems. The first problem is the mixed nonlinear-Neumann boundary value problem $$ \left\{ \begin{array}{ll} \displaystyle -\Delta…
In this work, we investigate the existence of positive solutions for a multi-point boundary value problem for a second order delay differential equation. Under certain growth conditions on the nonlinearity, and by the mean of Leray-Schauder…