Two-point boundary value problems for strongly singular higher-order linear differential equations with deviating arguments

Minimal periods of solutions to higher-order functional differential equations

“…New results on existence and uniqueness of periodic solutions for higher order functional differential equations are obtained in [25,26,27,28]. Note that Theorems 1 and 2 cannot be derived from these articles.…”

“…. ; if F satisfies ( 14) and there exists a non-constant solution to (5), then P = P n = max i=1,...,n p i L 1 satisfies the inequalities New results on existence and uniqueness of periodic solutions for higher order functional differential equations are obtained in [25,26,27,28]. Note that Theorems 1 and 2 cannot be derived from these articles.…”

A singular problem for functional differential equations with decreasing non‐linearities

“…In contrast to the case of ordinary differential equations, significantly less is known for singular equations with argument deviations. [9][10][11][12][13][14][15][16] The recent works [17][18][19][20] contain a thorough investigation of linear scalar functional differential equations with time singularities based on the study of the solution space of a model equation. 21 Singular initial value problems for non-linear equations have been studied mainly in the Volterra case.…”

The dirichlet boundary value problems for strongly singular higher-order nonlinear functional-differential equations

“…In the papers [18], [15] these results are generalized to linear differential equations with deviating arguments, i.e., the Agarwal-Kiguradze type theorems, which guarantee Fredholm's property for linear differential equations with deviating arguments are proved. In this paper, on the bases of articles [2] and [17] we prove the a priori boundedness principle for the problem (1.1), (1.2) in the case when the operator has the form (1.5).…”

“…Now we introduce some results from the articles [18], [15], which we need for this work. Consider the equation…”