Functional viability theorems for differential inclusions with memory
Functional-differential equations with Riemann-Liouville integrals in the nonlinearities
A sufficient condition for the nonexistence of blowing-up solutions to evolution functional-differential equations in Banach spaces with the Riemann-Liouville integrals in their right-hand sides is proved. The linear part of such type of equations is an infinitesimal generator of a strongly continuous semigroup of linear bounded operators. The proof of the main result is based on a desingularization method applied by the author in his papers on integral inequalities with weakly singular kernels....
Functions of finite fractional variation and their applications to fractional impulsive equations
We introduce a notion of a function of finite fractional variation and characterize such functions together with their weak -additive fractional derivatives. Next, we use these functions to study differential equations of fractional order, containing a -additive term—we prove existence and uniqueness of a solution as well as derive a Cauchy formula for the solution. We apply these results to impulsive equations, i.e. equations containing the Dirac measures.
Functions without residue and a bilinear differential equation
Fundamental central dispersion in a simple system
Fundamental central dispersions in a double system
Fundamental central dispersions of the phase function with the final oscillation
Fundamental quadratic splines and applications
Fundamental theorems for linear measure differential equations.
Further generalization of generalized quasilinearization method.
Further higher monotonicity properties of Sturm-Liouville functions
Suppose that the function in the differential equation (1) is decreasing on where . We give conditions on which ensure that (1) has a pair of solutions such that the -th derivative () of the function has the sign for sufficiently large and that the higher differences of a sequence related to the zeros of solutions of (1) are ultimately regular in sign.