On some nonlocal boundary value problems for nonlinear ordinary differential equations with delay
Journal Title: Дослідження в математиці і механіці - Year 2017, Vol 22, Issue 2
Abstract
The results of this paper were reported at International Workshop “Nonlinear Analysis and Nonautonomous Ordinary Differential Equations” (Odessa, Ukraine, June 23-27, 2017). In the paper, nonlocal boundary value problems are studied for higher order nonlinear ordinary differential equations with delay. More precisely, on a finite interval r𝑎,𝑏s, the differential equation 𝑢p𝑛qp𝑡q _ 𝑓p𝑡,𝑢p𝜏1p𝑡qq, . . . ,𝑢p𝑛_1qp𝜏𝑛p𝑡qqq is considered with the boundary conditions 𝑢p𝑖_1qp𝑎q _ 𝑐𝑖 p𝑖 _ 1, . . . ,𝑛 _ 1q, ℓp𝑢q _ 𝑐𝑛, where 𝑛 ¥ 2, 𝑓 : r𝑎,𝑏s _ R𝑛 Ñ R is a continuous function having continuous partial derivatives in the last 𝑛 arguments, 𝜏𝑖 : r𝑎,𝑏s Ñ r𝑎,𝑏s p𝑖 _ 1, . . . ,𝑛q are continuous functions satisfying the inequalities 𝜏𝑖p𝑡q ¤ 𝑡 for 𝑎 ¤ 𝑡 ¤ 𝑏 p𝑖 _ 1, . . . ,𝑛q, ℓ : 𝐶𝑛_1 pr𝑎,𝑏sq Ñ R is a linear bounded functional, and 𝑐𝑖 p𝑖 _ 1, . . . ,𝑛q are real constants. Sufficient conditions are established for the unique solvability of that problem. An analogue of Fredholm’s first theorem is obtained. The conditions of the main theorems guarantee also the well-posedness of that problem. An example is constructed showing the optimality of the obtained conditions. MSC: 34B10, 34B15.
Authors and Affiliations
N. Partsvania
Keywords
Related Articles
- EP ID EP343964
- DOI -
- Views 82
- Downloads 0
About the characteristic polynomial of product Frobenius’ matrix
The formula for calculating characteristic polynomials of product Frobenius’ matrix was obtained. The opportunity of using this formula by the tasks of control of nonlinear discret systems was shown.
AN ITERATIVE ALGORITHM FOR CALCULATION OF EIGENVALUES AND EIGENFUNCTIONS OF THE STURM--LIOUVILLE PROBLEM
An iterative algorithm for computing the i-th eigenvalue (e. v.) and the corresponding eigenfunction (e. f.) of the Sturm--Liouville problem on a finite interval is proposed. The algorithm uses the well-known asymptotic...
The sixth virial coefficient for the modified Lennard-Jones potential
In the wide range of dimensionless temperatures 0.2÷100, the sixth virial coefficient has been calculated for the modified Lennard-Jones potential (mLJ), which has a finite radius of interaction, while has no discontinui...
Nonlinear model of frictional impact of rigid body with rigid rough plane
Dynamics of reduced to the first order chain vibratory impact system with Coulomb friction is investigated. This system is suggested as a model of phenomena that occur under oblique impact of rigid body with perfectly ri...
On the oscillations in the quasi-linear second order differential systems with slowly-varying parameters
For the quasi-linear second order differential system with pure imaginary eigenvalues of the matrix of the linear part, the conditions of the existence of the particular solution, representable as an absolutely and unifo...