An abstract approach to some spectral problems of direct sum differential operators.
An abstract Cauchy problem for higher order functional differential inclusions with infinite delay
The existence results for an abstract Cauchy problem involving a higher order differential inclusion with infinite delay in a Banach space are obtained. We use the concept of the existence family to express the mild solutions and impose the suitable conditions on the nonlinearity via the measure of noncompactness in order to apply the theory of condensing multimaps for the demonstration of our results. An application to some classes of partial differential equations is given.
An abstract differential equation and the potential bifurcation theorems by Krasnosel'skij
An abstract differential inequality and eigenvalues of variational inequalities
An abstract existence result and its applications.
An abstract model of linear differential transformations
An abstract non-linear Cauchy-Kowalewski theorem and its proof by a contraction-mapping principle
An abstract nonlinear second order differential equation
By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of a semilinear second order differential initial value problem (1) as well as the existence of solutions of the linear inhomogeneous problem corresponding to (1) are proved. The main result of the paper is contained in Theorem 5.
An abstract semilinear first order differential equation in the hyperbolic case.
An abstract semilinear first order differential equation in the hyperbolic case
This paper is devoted to the investigation of the abstract semilinear initial value problem , in the “hyperbolic” case.
An adaptive continuation process for solving systems of nonlinear equations
An age-dependent model describing the spread of panleucopenia virus within feline populations
Global existence results and long time behavior are provided for a mathematical model describing the propagation of Feline Panleucopenia Virus (FPLV) within a domestic cat population; two transmission modes are involved: a direct one from infective cats to susceptible ones, and an indirect one from the contaminated environment to susceptible cats. A more severe impact of the virus on young cats requires an age-structured model.
An age-structured model of cannibalism.
An algebraic approach for solving boundary value matrix problems: existence, uniqueness and closed form solutions.
In this paper we show that in an analogous way to the scalar case, the general solution of a non homogeneous second order matrix differential equation may be expressed in terms of the exponential functions of certain matrices related to the corresponding characteristic algebraic matrix equation. We introduce the concept of co-solution of an algebraic equation of the type X^2 + A1.X + A0 = 0, that allows us to obtain a method of the variation of the parameters for the matrix case and further to find...
An Algebraic Approach to Implicit Evolution Equations
A Banach algebra homomorphism on the convolution algebra of integrable functions is the essence of Kisyński's equivalent formulation of the Hille-Yosida theorem for analytic semigroups. For the study of implicit evolution equations the notion of empathy happens to be more appropriate than that of semigroup. This approach is based upon the intertwining of two families of evolution operators and two families of pseudo-resolvents. In this paper we show that the Kisyński approach can be adapted to empathy...
An Algebraic Characterization of B-convergent Runge-Kutta Methods.
An algebraic condition for qualitative stability of first order linear autonomous ordinary differential systems
An algorithm for checking Hurwitz stability of K-symmetrizable interval matrices
An algorithm for detecting “linear” solutions of nonlinear polynomial differential equations.
An algorithm for determining the number of linearly independent comitants of a system of differential equations