Related papers: Fredholm Solvability of Time-Periodic Boundary Val…

This paper is concerned with the boundary-value problem on the Boltzmann equation in bounded domains with diffuse-reflection boundary where the boundary temperature is time-periodic. We establish the existence of time-periodic solutions…

We develop a linear theory of very weak solutions for nonlocal eigenvalue problems $\mathcal L u = \lambda u + f$ involving integro-differential operators posed in bounded domains with homogeneous Dirichlet exterior condition, with and…

We are concerned with global solutions of multidimensional Riemann problems for nonlinear hyperbolic systems of conservation laws, focusing on their global configurations and structures. We present some recent developments in the rigorous…

In this work, we study the well-posedness of the three dimensional magneto-hydrostatic equation under Grad-Rubin boundary value conditions. The proof relies on a fixed point argument to construct solutions to an elliptic-hyperbolic problem…

We provide fundamental properties of the first eigenpair for fractional $p$-Laplacian eigenvalue problems under singular weights, which is related to Hardy type inequality, and also show that the second eigenvalue is well-defined. We obtain…

The aim of this paper is to find the numerical solutions of the second order linear and nonlinear differential equations with Dirichlet, Neumann and Robin boundary conditions. We use the Bernoulli polynomials as linear combination to the…

In this paper, we study the nonlinear periodic Westervelt equation with excitations located within a bounded domain in $\mathbb{R}^d$, where $d \in \{2,3\}$, subject to Robin boundary conditions. This problem is of particular interest for…

For classical finite time horizon stopping problems driven by a Brownian motion \[V(t,x) = \sup_{t\leq\tau\leq0}E_{(t,x)}[g(\tau,W_{\tau})],\] we derive a new class of Fredholm type integral equations for the stopping set. For large problem…

In this paper, we analyze a second-order differential equation with a piecewise constant argument and reflection coupled to periodic boundary conditions. Our main contribution is the construction of the related Green's function and a…

We consider dynamic boundary conditions involving non-local operators. Our analysis includes a detailed description of such operators together with their relations with random times and random (additive) functionals. We provide some new…

Any numerical method fails to provide us with acceptable results if not equipped with appropriate boundary conditions. Catering to more realistic applications, in the present article we have extended the work done on the one plus one…

We consider a class of nonlinear Klein-Gordon equations which are Hamiltonian and are perturbations of linear dispersive equations. The unperturbed dynamical system has a bound state, a spatially localized and time periodic solution. We…

We provide a framework to build periodic boundary conditions on the pseudosphere (or hyperbolic plane), the infinite two-dimensional Riemannian space of constant negative curvature. Starting from the common case of periodic boundary…

This paper presents a new technique to investigate the existence of solutions to fractional three-point boundary value problems at resonance in a Hilbert space. Based on the proposed method, the restricted conditions…

This article is concerned with the existence and uniqueness of solutions to some fractional order boundary value problems. Our results are based on some fixed point theorems. For the applicability of our results, we provide an example.

This paper studies the dynamical behavior of classical solutions to a hyperbolic system of balance laws, derived from a chemotaxis model with logarithmic sensitivity, subject to time-dependent boundary conditions. It is shown that under…

Using the theory of fixed point index, we establish new results for the existence of nonzero solutions of Hammerstein integral equations with reflections. We apply our results to a first order periodic boundary value problem with…

In a class of inner product H\"ormander spaces, we investigate a general elliptic problem for which the maximum of orders of boundary conditions is grater than or equal to the order of elliptic equation. The order of regularity for these…

A unified general approach is presented for construction of solutions of the characteristic initial value problems for various integrable hyperbolic reductions of Einstein's equations for space-times with two commuting isometries in General…

The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit…