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Finsler's lemma is a classic mathematical result with applications in control and optimization. When the lemma is applied to parameter-dependent LMIs, as such those that arise from problems of robust stability, the extra variables…
We investigate regularity properties of the $\overline{\partial}$-equation on domains in a complex euclidean space that depend on a parameter. Both the interior regularity and the regularity in the parameter are obtained for a continuous…
The well-known solution theory for (systems of) linear ordinary differential equations undergoes significant changes when introducing an additional real parameter. Properties like the existence of fundamental sets of solutions or…
An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an…
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…
We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form $\m{A}x=\lambda\m{B}x$, where the matrices $\m{A}$ and/or $\m{B}$ may depend on a scalar parameter.…
We investigate the dependence on parameters for the discrete boundary value problem connected with the Emden-Fowler equation. A variational method is used in order to obtain a general scheme allowing for investigation the dependence on…
We consider the most general class of linear boundary-value problems for higher-order ordinary differential systems whose solutions and right-hand sides belong to the corresponding Sobolev spaces. For parameter-dependent problems from this…
We show that parameterized versions of splitting theorems in Morse theory can be effectively used to generalize some famous bifurcation theorems for potential operators. In particular, such generalizations based on the author's recent…
An iteration-free method of domain decomposition is considered for approximate solving a boundary value problem for a second-order parabolic equation. A standard approach to constructing domain decomposition schemes is based on a partition…
This is the second part of a series devoting to the generalizations and applications of common theorems in variational bifurcation theory. Using abstract theorems in the first part we obtain many new bifurcation results for quasi-linear…
We investigate the dependence on parameters for second order difference equations with two point boundary value conditions by using a variational method in case when the corresponding Euler action functional is coercive. Some applications…
The construction of stochastic solutions for nonlinear partial differential equations is a powerful method to obtain new exact results and to develop efficient numerical algorithms, in particular when domain decomposition techniques are…
We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric…
A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
In this paper, we present a new matrix approach for the analysis of subdivision schemes whose non-stationarity is due to linear dependency on parameters whose values vary in a compact set. Indeed, we show how to check the convergence in…
This is the first part of a series devoting to the generalizations and applications of common theorems in variational bifurcation theory. Using parameterized versions of splitting theorems in Morse theory we generalize some famous…
The necessary and sufficient conditions for a function to be totally or partially separable are derived. It is shown that a function is totally separable if and only if each component of the gradient vector of depends only on the…
The aim of this paper is to study certain problems of calculus of variations, that are dependent upon a Lagrange function on a Caputo-type fractional derivative. This type of fractional operator is a generalization of the Caputo and the…