Related papers: New Algebraic Approaches to Classical Boundary Lay…
In this note we discuss an abstract framework for standard boundary value problems in divergence form with maximal monotone relations as "coefficients". A reformulation of the respective problems is constructed such that they turn out to be…
The main goal of this paper is the study of two kinds of nonlinear problems depending on parameters in unbounded domains. Using a nonstandard variational approach, we first prove the existence of bounded solutions for nonlinear eigenvalue…
This work presents results on the boundary properties of solutions of a complex, planar, smooth vector field $L$. Classical results in the $H^p$ theory of holomorphic functions of one variable are extended to the solutions of a class of…
For a wave equation with pure delay, we study an inhomogeneous initial-boundary value problem in a bounded 1D domain. Under smoothness assumptions, we prove unique existence of classical solutions for any given finite time horizon and give…
We discuss a Lie algebraic and differential geometry construction of solutions to some multidimensional nonlinear integrable systems describing diagonal metrics on Riemannian manifolds, in particular those of zero and constant curvature.…
A new technique is presented to solve a class of linear boundary value problems (BVP). Technique is primarily based on an operational matrix developed from a set of modified Bernoulli polynomials. The new set of polynomials is an…
We investigate classical solutions of nonlinear elliptic equations with two classes of dynamical boundary conditions, of reactive and reactive-diffusive type. In the latter case it is shown that well-posedness is to a large extent…
An important problem that arises in many engineering applications is the boundary value problem for ordinary differential equations. There have been many computational methods proposed for dealing with this problem. The convergence of the…
This paper deals with the boundary value problems for the singularly perturbed differential-algebraic system of equations. The case of turning points has been studied. The sufficient conditions for existence and uniqueness of the solution…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Under a Morse index condition we prove symmetry results for solutions of a nonlinear mixed boundary condition elliptic problem. As an intermediate step we relate the Morse index of a solution to a mixed boundary condition linear eigenvalue…
The Material Point Method (MPM) is a hybrid Eulerian-Lagrangian approach capable of simulating large deformation problems of history-dependent materials. While the MPM can represent complex and evolving material domains by using Lagrangian…
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…
Nonstationary and nonequilibrium processes are considered on the basis of an Enskog-Landau kinetic equation using a boundary conditions method. A nonstationary solution of this equation is found in the pair collision approximation. This…
We introduce new methods for the numerical solution of general Hamiltonian boundary value problems. The main feature of the new formulae is to produce numerical solutions along which the energy is precisely conserved, as is the case with…
Second order nonlinear eigenvalue problems are considered for which the spectrum is an interval. The boundary conditions are of Robin and Dirichlet type. The shape and the number of solutions are discussed by means of a phase plane…
We prove well-posedness and regularity results for elliptic boundary value problems on certain domains with a smooth set of singular points. Our class of domains contains the class of domains with isolated oscillating conical singularities,…
We review our algebraic framework for linear boundary problems (concentrating on ordinary differential equations). Its starting point is an appropriate algebraization of the domain of functions, which we have named integro-differential…
A new definition of conditional invariance for boundary value problems involving a wide range of boundary conditions (including initial value problems as a special case) is proposed. It is shown that other definitions worked out in order to…
Using Leray-Schauder degree theory we study the existence of at least one solution for the boundary value problem of the type (\varphi(u' ))' = f(t,u,u'), u'(0)=u(0), u'(T)= bu'(0), where \varphi is a homeomorphism such that \varphi(0)=0, f…