TY - JOUR
T1 - On a boundary value problem for integro-differential equations on the halfline
AU - Domoshnitsky, A.
AU - Koplatadze, R.
PY - 2009/1/15
Y1 - 2009/1/15
N2 - The following boundary value problem (0.1)x′ (t) = p (t) ∫0σ (t) q (s) x (τ (s)) d s,(0.2)x (t) = φ (t) for t ∈ [τ0, 0), under(lim inf, t → + ∞) | x (t) | < + ∞ is considered, where p ∈ C (R+ ; (0, + ∞)), q ∈ Lloc (R+ ; R+), 0 ≤ σ (t) ≤ t, τ (t) < t for t ∈ R+, limt → + ∞ σ (t) = limt → + ∞ τ (t) = + ∞, τ0 = inf {τ (t) : t ∈ R+}, φ ∈ C ([τ0, 0)) and sup {{divides} φ (t) {divides} : t ∈ [τ0, 0)} < + ∞. Sufficient conditions are obtained for problem (0.1) and (0.2) to have a solution, a unique solution and a unique oscillatory solution.
AB - The following boundary value problem (0.1)x′ (t) = p (t) ∫0σ (t) q (s) x (τ (s)) d s,(0.2)x (t) = φ (t) for t ∈ [τ0, 0), under(lim inf, t → + ∞) | x (t) | < + ∞ is considered, where p ∈ C (R+ ; (0, + ∞)), q ∈ Lloc (R+ ; R+), 0 ≤ σ (t) ≤ t, τ (t) < t for t ∈ R+, limt → + ∞ σ (t) = limt → + ∞ τ (t) = + ∞, τ0 = inf {τ (t) : t ∈ R+}, φ ∈ C ([τ0, 0)) and sup {{divides} φ (t) {divides} : t ∈ [τ0, 0)} < + ∞. Sufficient conditions are obtained for problem (0.1) and (0.2) to have a solution, a unique solution and a unique oscillatory solution.
KW - Boundary value problem
KW - Oscillation
KW - Proper solution
UR - http://www.scopus.com/inward/record.url?scp=71649103637&partnerID=8YFLogxK
U2 - 10.1016/j.na.2009.07.026
DO - 10.1016/j.na.2009.07.026
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AN - SCOPUS:71649103637
SN - 0362-546X
VL - 72
SP - 836
EP - 846
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
IS - 2
ER -