Related papers: Discontinuous functional differential equations wi…
We prove a global continuation result for $T$-periodic solutions of a $T$-periodic parametrized second order retarded functional differential equation on a boundaryless compact manifold with nonzero Euler-Poincare' characteristic. The…
The fundamental matrix and the delay Lyapunov matrix of linear delay difference equations are introduced. Some properties of the Lyapunov matrix, and the jump discontinuities of its derivative are proven, leading to its construction in the…
We obtain conditions for existence of unique global or maximally extended solutions to generalized neural field equations. We also study continuous dependence of these solutions on the spatiotemporal integration kernel, delay effects,…
A meromorphic solution of a complex linear differential equation (with meromorphic coefficients) for which the value zero is the only possible finite deficient/deviated value is called a standard solution. Conditions for the existence and…
The well-posedness of a system of partial differential equations and dynamic boundary conditions, both of Cahn-Hilliard type, is discussed. The existence of a weak solution and its continuous dependence on the data are proved using a…
In this work, a mixed problem for a time-fractional equation with a delayed argument and pseudodifferential operators related to Laplace operators with non-local boundary conditions in Sobolev classes is studied. The solutions to the…
Second order linear non-autonomous differential equations with negative stiffness are considered. Using Chetaev-like (Lyapunov-like) functions, necessary (sufficient) conditions are found for the solutions to be bounded for all initial…
Approximation techniques have been historically important for solving differential equations, both as initial value problems and boundary value problems. The integration of numerical, analytic and perturbation methods and techniques can…
This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. System-theoretic results are provided for both classes of…
Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential…
We study two classes of linear difference differential equations analogous to Euler-Cauchy ordinary differential equations, but in which multiple arguments are shifted forward or backward by fixed amounts. Special cases of these equations…
In this paper, we establish the existence of a positive, bounded solution for a class of parabolic partial differential equations with nonlinear boundary conditions, where the boundary conditions depend on the solution on the boundary at a…
In this article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…
We study uniqueness of solutions to degenerate parabolic problems, posed in bounded domains, where no boundary conditions are imposed. Under suitable assumptions on the operator, uniqueness is obtained for solutions that satisfy an…
In this work, the Dirac-type integro di{\S}erential system with one classical boundary condition and another nonlocal integral boundary condition is considered. We obtain the asymptotic formulae for the solutions, eigenvalues and nodal…
A class of first order linear impulsive differential equation with continuous and piecewise constant arguments is studied. Sufficient conditions for the oscillation of the solutions are obtained.
The problem of algebraic dependence of solutions to (non-linear) first order autonomous equations over an algebraically closed field of characteristic zero is given a `complete' answer, obtained independently of model theoretic results on…
Fractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
In this paper, we consider the Laplace equation with a class of indefinite superlinear boundary conditions and study the uniqueness of positive solutions that this problem possesses. Superlinear elliptic problems can be expected to have…