中山大学学报（自然科学版）
中山大學學報（自然科學版）
중산대학학보（자연과학판）
ACTA SCIENTIARUM NATURALIUM UNIVERSITATIS SUNYATSENI
2009年
6期
23-26
,共4页
二阶非线性时标动态方程%非振动解%存在性%中立型%Krasnoselskii不动点定理
二階非線性時標動態方程%非振動解%存在性%中立型%Krasnoselskii不動點定理
이계비선성시표동태방정%비진동해%존재성%중립형%Krasnoselskii불동점정리
second-order nonlinear dynamic equations on time scales%nonoscillatory solutions%existence%neutral%Krasnoselskii's fixed point theorem
利用Krasnoselskii不动点定理,建立了研究二阶非线性中立型时标动态方程[r(t)(x(t)+p(t)x(t-τ))~Δ]~Δ+∑_(i=1)~mQi(t)f_i(x(t-σ_i))=0, t∈T的非振动解的存在性条件.所得结果包含二阶非线性中立型微分方程相应的结论,并给出二阶非线性中立型差分方程新的判别准则.
利用Krasnoselskii不動點定理,建立瞭研究二階非線性中立型時標動態方程[r(t)(x(t)+p(t)x(t-τ))~Δ]~Δ+∑_(i=1)~mQi(t)f_i(x(t-σ_i))=0, t∈T的非振動解的存在性條件.所得結果包含二階非線性中立型微分方程相應的結論,併給齣二階非線性中立型差分方程新的判彆準則.
이용Krasnoselskii불동점정리,건립료연구이계비선성중립형시표동태방정[r(t)(x(t)+p(t)x(t-τ))~Δ]~Δ+∑_(i=1)~mQi(t)f_i(x(t-σ_i))=0, t∈T적비진동해적존재성조건.소득결과포함이계비선성중립형미분방정상응적결론,병급출이계비선성중립형차분방정신적판별준칙.
By employing Krasnoselskii's fixed point theorem, the existence of nonoscillatory solutions of the second-order nonlinear neutral dynamic equations on time scales
[r(t)(x(t)+p(t)x(t-τ))~Δ]~Δ+ ∑_(i=1)~mQ_i(t)f_i(x(t-σ_i)) = 0,t∈T is established. The obtained results cover those for second-order nonlinear neutral differential equations and provide new crtteria for second-order nonlinear neutral differential equations.
