The generalized Cauchy problem for singularly perturbed impulsive systems in the critical case.
The generalized de Rham-Hodge theory aspects of Delsarte-Darboux type transformations in multidimension
The differential-geometric and topological structure of Delsarte transmutation operators and their associated Gelfand-Levitan-Marchenko type eqautions are studied along with classical Dirac type operator and its multidimensional affine extension, related with selfdual Yang-Mills eqautions. The construction of soliton-like solutions to the related set of nonlinear dynamical system is discussed.
The generalized method of quasilinearization and nonlinear boundary value problems with integral boundary conditions.
The generalized Turner-Bradley-Kirk-Pruitt equation.
The geometry of convex cones associated with the Lyapunov inequality and the common Lyapunov function problem.
The HELP inequality for Hamiltonian systems.
The H-theorem for Boltzmann type equations.
The initial boundary value problem of a mixed-typed hemivariational inequality.
The Interaction Between instability and Local Truncation Error Estimate for Predictor - Corrector Methods
The intervals of stability of Runge-Kutta methods after Richardson extrapolation
The inverse carrier problem
The problem was motivated by Borůvka’s definitions of the carrier and the associated carrier. The inverse carrier problem is precisely defined and partially solved. Examples are given.
The inverse spectral problem for the Sturm-Liouville operators with discontinuous coefficients.
The linear Cauchy problem for a class of differential equations with distributional coefficients.
The lower and upper solutions method for first order differential inclusions with nonlinear boundary conditions.
The Massera-Schäffer problem for a first order linear differential equation
We consider the Massera-Schäffer problem for the equation where and By...
The method of normal splines for linear implicit differential equations of second order.
The method of quasi-linearization for resolution a nonlocal nonlinear boundary problem.
The method of solution of the boundary value problem applied to a certain fourth order differential equation
The method of upper and lower solutions for Carathéodory -th order differential inclusions.
The method of upper and lower solutions for partial hyperbolic fractional order differential inclusions with impulses
In this paper we use the upper and lower solutions method to investigate the existence of solutions of a class of impulsive partial hyperbolic differential inclusions at fixed moments of impulse involving the Caputo fractional derivative. These results are obtained upon suitable fixed point theorems.