Related papers: Linear theory for a mixed operator with Neumann co…
We study positive solutions of semilinear elliptic equations in a planar triangular domain under mixed boundary conditions, consisting of homogeneous Dirichlet boundary conditions on one side and homogeneous Neumann boundary conditions on…
The Dirichlet-to-Neumann map associated to an elliptic partial differential equation becomes multivalued when the underlying Dirichlet problem is not uniquely solvable. The main objective of this paper is to present a systematic study of…
We prove Li-Yau-Kr\"oger type bounds for Neumann-type eigenvalues of the poly-harmonic operator and of the biharmonic operator on bounded domains in a Euclidean space. We also prove sharp estimates for lower order eigenvalues of a…
We consider Dirac-type operators on manifolds with boundary, and set out to determine all local smooth boundary conditions that give rise to (strongly) regular self-adjoint operators. By combining the general theory of boundary value…
We study a Neumann type initial-boundary value problem for strongly degenerate parabolic-hyperbolic equations under the nonlinearity-diffusivity condition. We suggest a notion of entropy solution for this problem and prove its uniqueness.…
In this paper, we present a novel framework to solve differential equations based on multilayer feedforward network. Previous works indicate that solvers based on neural network have low accuracy due to that the boundary conditions are not…
In this paper we are concerned with the initial boundary value problems of linear and semi-linear parabolic equations with mixed boundary conditions on non-cylindrical domains in spatial-temporal space. We obtain the existence of a weak…
We explore singular second-order boundary value problems with mixed boundary conditions on a general time scale. Using the lower and upper solutions method combined with the Brouwer fixed point theorem we demonstrate the existence of a…
The Graetz problem is a convection-diffusion equation in a pipe invariant along a direction. The contribution of the present work is to propose a mathematical analysis of the Neumann, Robin and periodic boundary condition on the boundary of…
We establish the existence and uniqueness of solutions for quasilinear singular Lane-Emden type systems subjected to Neumann boundary conditions. The approach is chiefly based on sub-supersolutions method.
Classical results of second order parabolic quasi-linear equations always require that the nonlinear terms are controlled by a power of the unknown functions and their first derivatives. We improve the previous results. More precisely, in…
This paper concerns the eigenvalues of the Neumann-Poincar\'e operator, a boundary integral operator associated with the harmonic double-layer potential. Specifically, we examine how the eigenvalues depend on the support of integration and…
We propose a new approach to the spectral theory of perturbed linear operators , in the case of a simple isolated eigenvalue. We obtain two kind of results: ''radius bounds'' which ensure perturbation theory applies for perturbations up to…
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded semidefinite perturbation is considered. A variant of the Davis-Kahan $ \sin2\Theta $ theorem from [SIAM J. Numer. Anal. 7 (1970), 1--46]…
The paper considers the general form of self-adjoint boundary value problems for momentum operators with nonlocal potentials. We give an analysis of the eigenvalue distribution as zeros of the characteristic functions, for which their…
We apply the linking method for cones in normed spaces to p-Laplace equations with various nonlinear boundary conditions. Some existence results are obtained.
Sum of a second derivative operator with periodic boundary conditions and an integral operator of rank one (non-local potential) is studied in this manuscript. Not only spectral analysis is conducted for this operator but the inverse…
The boundary-value problem on semi-axis for one class operator-differential equations of the fourth order, the main part of which has the multiple characteristic is investigated in this paper in Sobolev type weighted space. Correctness and…
Machine-learning based methods like physics-informed neural networks and physics-informed neural operators are becoming increasingly adept at solving even complex systems of partial differential equations. Boundary conditions can be…
In his deep and prolific investigations of heat diffusion, Lam\'e was led to the investigation of the eigenvalues and eigenfunctions of the Laplace operator in an equilateral triangle. In particular he derived explicit results for the…