On Some Properties of Solutions of Second Order Linear Functional Differential Equations
-
I. Kiguradze
Abstract
The properties of solutions of the equation
u″(t) =
p1
(t)u(τ1(t))
+
p2(t)u′(τ2(t)) are investigated where
pi: [a,
+∞[→ R (i
= 1, 2) are locally summable functions,
τ1 : [a,
+∞[→ R is a measurable
function and τ2 :
[a, +∞[→
R is a nondecreasing locally absolutely continuous one.
Moreover, τi(t) ≥ t (i
= 1, 2), p1 (t) ≥
0, 
,
ε = const > 0 and
. In particular, it is
proved that solutions whose derivatives are square integrable on
[a, +∞ [ form a
one-dimensional linear space and for any such solution to vanish at infinity it
is necessary and sufficient that 
.
© 1994 Plenum Publishing Corporation
Articles in the same Issue
- Boundary Value Problems of Electroelasticity with Concentrated Singularities
- Passage of the Limit Through the Double Denjoy Integral
- On Some Properties of Solutions of Second Order Linear Functional Differential Equations
- Generalized Sierpinski Sets
- Two-Weighted Estimates for Some Integral Transforms in the Lebesgue Spaces with Mixed Norm and Imbedding Theorems
- Linear Dynamical Systems of Higher Genus
- On the Durrmeyer-Type Modification of Some Discrete Approximation Operators
- Fractional Type Operators in Weighted Generalized Hölder Spaces
- Complexity of the Decidability of the Unquantified Set Theory with A Rank Operator
- On Perfect Mappings from ℝ to ℝ
Articles in the same Issue
- Boundary Value Problems of Electroelasticity with Concentrated Singularities
- Passage of the Limit Through the Double Denjoy Integral
- On Some Properties of Solutions of Second Order Linear Functional Differential Equations
- Generalized Sierpinski Sets
- Two-Weighted Estimates for Some Integral Transforms in the Lebesgue Spaces with Mixed Norm and Imbedding Theorems
- Linear Dynamical Systems of Higher Genus
- On the Durrmeyer-Type Modification of Some Discrete Approximation Operators
- Fractional Type Operators in Weighted Generalized Hölder Spaces
- Complexity of the Decidability of the Unquantified Set Theory with A Rank Operator
- On Perfect Mappings from ℝ to ℝ
