Related papers: Multivalued nonmonotone dynamic boundary condition
In this paper, we derive the approximate controllability of fractional evolution hemivariational inequalities in reflexive Banach spaces involving Caputo fractional derivatives. We first show that the original problem is connected with a…
Mixed optimal stopping and stochastic control problems define variational inequalities with non-linear Hamilton-Jacobi-Bellman (HJB) operators, whose numerical solution is notoriously difficult and lack of reliable benchmarks. We first use…
We consider linear and obstacle problems driven by a nonlocal integral operator, for which nonlocal interactions are restricted to a ball of finite radius. These type of operators are used to model anomalous diffusion and, for a special…
In this paper we continue our study of bifurcations of solutions of boundary-value problems for symplectic maps arising as Hamiltonian diffeomorphisms. These have been shown to be connected to catastrophe theory via generating functions and…
We consider a Laplacian on the one-sided full shift space over a finite symbol set, which is constructed as a renormalized limit of finite difference operators. We propose a weak definition of this Laplacian, analogous to the one in…
We present boundary-integral equations for Maxwell-type problems in a differential-form setting. Maxwell-type problems are governed by the differential equation $(\delta\mathrm{d}-k^2)\omega = 0$, where $k\in\mathbb{C}$ holds, subject to…
In the first part of the paper boundary-value problems are considered under weak assumptions on the smoothness of the domains. We assume nothing about smoothness of the boundary $\partial D$ of a bounded domain $D$ when the homogeneous…
In the first part of this article we deal with the existence of at least three non-trivial weak solutions of a nonlocal problem with nonstandard growth involving a nonlocal Robin type boundary condition. The second part of the article is…
This paper introduces a new class of variational inequalities where the obstacle is placed in the exterior domain that is disjoint from the observation domain. This is carried out with the help of nonlocal fractional operators. The need for…
For the evolutionary Stokes problem with dynamic boundary conditions, we show the maximal regularity of weak solutions in time. Due to the characterization of $R$-sectorial operators on Hilbert spaces, the proof reduces to identifying the…
We adapt boundary deformation techniques to solve a Neumann problem for the Helmholtz equation with rough electric potentials in bounded domains. In particular, we study the dependance of Neumann eigenvalues of the perturbed Laplacian with…
Variational-hemivariational inequalities are an area full of interesting and challenging mathematical problems. The area can be viewed as a natural extension of that of variational inequalities. Variational-hemivariational inequalities are…
This paper is concerned with a class of partial differential equations, which are the linear combinations, with constant coefficients, of the classical flows of the KdV hierarchy. A boundary value problem with inhomogeneous boundary…
On a bounded Lipschitz domain we consider two selfadjoint operator realizations of the same second order elliptic differential expression subject to Robin boundary conditions, where the coefficients in the boundary conditions are functions.…
In this work, we introduce a novel variational framework for the study of the unsteady Stokes equations in a bounded open Lipschitz domain in R^n, involving a Caputo fractional derivative in time. The nonlocal nature of the fractional…
We study the boundary control of solutions of the Helmholtz and Maxwell equations to enforce local non-zero constraints. These constraints may represent the local absence of nodal or critical points, or that certain functionals depending on…
Inspired by recent developments in the theory of stability results in the context of certain wave type phenomena, we discuss abstract damped hyperbolic type equations given in a block operator matrix form with regards to asymptotic…
The eigenvalues of the Laplace-Beltrami operator and the integrals of products of eigenfunctions must satisfy certain consistency conditions on compact Riemannian manifolds. These consistency conditions are derived by using spectral…
This manuscript is devoted to the study of a class of nonlinear non-instantaneous impulsive first order abstract retarded type functional differential equations in an arbitrary separable Hilbert space H. A new set of sufficient conditions…
The paper develops a theory of spectral boundary value problems from the perspective of general theory of linear operators in Hilbert spaces. An abstract form of spectral boundary value problem with generalized boundary conditions is…