The Central Connection Problem at Turning Points of Linear Differential Equations
The characteristic multipliers of a block and of an inverse block of second-order linear differential equations with -periodic coefficients
The constants of the Volterra derivation
The ring of constants of the Volterra derivation is found. Confirming a conjecture of Zielinski, it is always a polynomial ring.
The differential form method for finding symmetries.
The distance between fixed points of some pairs of maps in Banach spaces and applications to differential systems
Let be a -contraction on a Banach space and let be an almost -contraction, i.e. sum of an -contraction with a continuous, bounded function which is less than in norm. According to the contraction principle, there is a unique element in for which If moreover there exists in with , then we will give estimates for Finally, we establish some inequalities related to the Cauchy problem.
The Drazin inverse in multibody system dynamics.
The dynamics of the drum mower blade
The drum mower blade is freely rotatable around the fastening pin. During the operation of the mower, the centrifugal force and the resistance of the mowing material act on it. The presented article studies the effect of these forces on the behavior of the blade, in particular its oscillation around the steady state, depending on the properties of the cut material.
The effect of infinitesimal damping on the dynamic instability mechanism of conservative systems.
The eigenvalues of symmetric Sturm-Liouville problem and inverse potential problem, based on special matrix and product formula
The Sturm-Liouville eigenvalue problem is symmetric if the coefficients are even functions and the boundary conditions are symmetric. The eigenfunction is expressed in terms of orthonormal bases, which are constructed in a linear space of trial functions by using the Gram-Schmidt orthonormalization technique. Then an -dimensional matrix eigenvalue problem is derived with a special matrix , that is, if is odd.Based on the product formula, an integration method with a fictitious time, namely...
The equation in when is quasi-invertible
The Equivalence Of Certain Linear And Nonlinear Differential Equations Of N-th Order
The existence and the uniqueness of distributional solutions of some systems of non-linear differential equations
The existence of positive solution to a nonlinear fractional differential equation with integral boundary conditions.
The existence of positive solution to three-point singular boundary value problem of fractional differential equation.
The first, the second, and the third Liouville formula and periodical solutions of linear differential equation of the second order
The formal solution of Mikusiński operational differential equations with variable coefficients.
The General Differential Operators Generated by a Quasi-Differential Expressions with their Interior Singular Points
The general ordinary quasi-differential expression M of n-th order with complex coefficients and its formal adjoint M + are considered over a regoin (a, b) on the real line, −∞ ≤ a < b ≤ ∞, on which the operator may have a finite number of singular points. By considering M over various subintervals on which singularities occur only at the ends, restrictions of the maximal operator generated by M in L2|w (a, b) which are regularly solvable with respect to the minimal operators T0 (M ) and T0...
The general solution of impulsive systems with Riemann-Liouville fractional derivatives
In this paper, we study a kind of fractional differential system with impulsive effect and find the formula of general solution for the impulsive fractional-order system by analysis of the limit case (as impulse tends to zero). The obtained result shows that the deviation caused by impulses for fractional-order system is undetermined. An example is also provided to illustrate the result.
The generalised ellipsoidal wave equation [0,3,11].
Explicit solutions are obtained of the linear differential equation of the second order with three regular singularities and one irregular singularity of the first type. The behavior at the point at infinity is discussed. An important special case is an algebraic form of the ellipsoidal wave equation.
The generalized approximation method and nonlinear heat transfer equations.