The semilinear Feng and FMV spectra.
The set of first-order differential equations with periodic or bounded solutions.
The objective of this note is the announcement of two results of Ambrosetti-Prodi type concerning the existence of periodic (respectively bounded) solutions of the first order differential equation x' = f (t,x).
The set of recurrent points of a continuous self-map on compact metric spaces and strong chaos
We discuss the existence of an uncountable strongly chaotic set of a continuous self-map on a compact metric space. It is proved that if a continuous self-map on a compact metric space has a regular shift invariant set then it has an uncountable strongly chaotic set in which each point is recurrent, but is not almost periodic.
The shadowing chain lemma for singular Hamiltonian systems involving strong forces
We consider a planar autonomous Hamiltonian system :q+∇V(q) = 0, where the potential V: ℝ2 {ζ→ ℝ has a single well of infinite depth at some point ζ and a strict global maximum 0at two distinct points a and b. Under a strong force condition around the singularity ζ we will prove a lemma on the existence and multiplicity of heteroclinic and homoclinic orbits - the shadowing chain lemma - via minimization of action integrals and using simple geometrical arguments.
The shooting approach in analyzing bang-bang extremals with simultaneous control switches
The shooting method and multiple solutions of two/multi-point BVPs of second-order ODE.
The shooting method and nonhomogeneous multipoint bvps of second-order ODE.
The singular Cauchy-Nicoletti problem for the system of two ordinary differential equations
In the paper the singular Cauchy-Nicoletti problem for the system ot two ordinary differential equations is considered. New sufficient conditions for solvability of this problem are proved. In the proofs the topological method is applied. Some comparisons with known results are also given in the paper.
The solution existence and convergence analysis for linear and nonlinear differential-operator equations in Banach spaces within the Calogero type projection-algebraic scheme of discrete approximations
The projection-algebraic approach of the Calogero type for discrete approximations of linear and nonlinear differential operator equations in Banach spaces is studied. The solution convergence and realizability properties of the related approximating schemes are analyzed. For the limiting-dense approximating scheme of linear differential operator equations a new convergence theorem is stated. In the case of nonlinear differential operator equations the effective convergence conditions for the approximated...
The solution of parabolic models by finite element space and -stable time discrezation
The solution of the initial value problem for the general dynamic equations in nonlinear elasticity under damping conditions
The solution of the two-point boundary value problem for a nonlinear differential equation of the third order
The solution of two-point boundary value problem of a class of Duffing-type systems with non- perturbation term.
The solution operator for a partial differential equation with delay
Viene dimostrata l’esistenza e l’unicità globale della soluzione di un’equazione funzionale in uno spazio di Hilbert e si caratterizza il generatore infinitesimale del semigruppo ad essa associato. Il risultato è applicato ad equazioni integrodifferenziali a derivate parziali di tipo parabolico in cui compaiono argomenti con ritardo (discreto e continuo) nelle derivate spaziali di ordine massimo.
The solution set of a differential inclusionon a closed set of a Banach space
We consider differential inclusions with state constraints in a Banach space and study the properties of their solution sets. We prove a relaxation theorem and we apply it to prove the well-posedness of an optimal control problem.
The spectra of general differential operators in the direct sum spaces
In this paper, the general ordinary quasi-differential expression of -th order with complex coefficients and its formal adjoint on any finite number of intervals , , are considered in the setting of the direct sums of -spaces of functions defined on each of the separate intervals, and a number of results concerning the location of the point spectra and the regularity fields of general differential operators generated by such expressions are obtained. Some of these are extensions or generalizations...
The spectral approximation for the shock layer problems.
The Spectrum of Hill's Equation.
The spectrum of the damped wave operator for a bounded domain in .
The stability analysis of a discretized pantograph equation
The paper deals with a difference equation arising from the scalar pantograph equation via the backward Euler discretization. A case when the solution tends to zero but after reaching a certain index it loses this tendency is discussed. We analyse this problem and estimate the value of such an index. Furthermore, we show that the utilized proof technique enables us to investigate some other numerical formulae, too.