where Ï‰ > 0, : C([0,Ï‰]) â†’ L([0,Ï‰]) is a linear bounded operator and q âˆˆ L([0,Ï‰]). By a solution of the problem (1.1), (1.2) we understand a function u âˆˆ CÌƒâ€²([0,Ï‰]), which satisfies (1.1) almostâ€¦ (More)

Problems on the existence and uniqueness of a periodic solution of nonautonomous ordinary differential equations and systems have long been attracting the attention of mathematicians and used as theâ€¦ (More)

In the present paper, we consider nonlinear functional differential inequalities appearing in the theory of boundary value problems (see [1]â€“[6] and the references therein) and formulate new resultsâ€¦ (More)

For strongly singular higher-order differential equations with deviating arguments, under two-point conjugated and right-focal boundary conditions, AgarwalKiguradze type theorems are established,â€¦ (More)

For strongly singular higher-order differential equations with deviating arguments, under nonlocal boundary conditions, Agarwal-Kiguradze type theorems are established, which guarantee the presenceâ€¦ (More)

On the rectangleD = [a, b]Ã—[c, d], the problem on the existence and uniqueness of a nonnegative solution of the characteristic initial value problem for the equation âˆ‚2u(t, x) âˆ‚t âˆ‚x = `(u)(t, x)+â€¦ (More)

Efficient sufficient conditions are established for the solvability of the Dirichlet problem uâ€²â€²(t) = p(t)u(t) + f(t, u(t)) + h(t) for a â‰¤ t â‰¤ b, u(a) = 0, u(b) = 0, where h, p âˆˆ L([a, b];R) and f âˆˆâ€¦ (More)

Unimprovable effective sufficient conditions are established for the unique solvability of the periodic problem ui(t) = i+1 âˆ‘ j=2 `i,j(uj)(t) + qi(t) for 1 â‰¤ i â‰¤ nâˆ’ 1, un(t) = n âˆ‘ j=1 `n,j(uj)(t) +â€¦ (More)