About Positivity of Green's Functions for Nonlocal Boundary Value Problems with Impulsive Delay Equations
The impulsive delay differential equation is considered (Lx)(t)=x′(t)+∑i=1mpi(t)x(t-τi(t))=f(t), t∈[a,b], x(tj)=βjx(tj-0), j=1,…,k, a=t0<t1<t2<⋯<tk<tk+1=b, x(ζ)=0, ζ∉[a,b], with nonlocal boundary condition lx=∫abφsx′sds+θxa=c, φ∈L∞a,b; θ, c∈R. Various results on existence and uniqu...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/978519 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | The impulsive delay differential equation is considered (Lx)(t)=x′(t)+∑i=1mpi(t)x(t-τi(t))=f(t), t∈[a,b], x(tj)=βjx(tj-0), j=1,…,k, a=t0<t1<t2<⋯<tk<tk+1=b, x(ζ)=0, ζ∉[a,b], with nonlocal boundary condition lx=∫abφsx′sds+θxa=c, φ∈L∞a,b; θ, c∈R. Various results on existence and uniqueness of solutions and on positivity/negativity of the Green's functions for this equation are obtained. |
|---|---|
| ISSN: | 2356-6140 1537-744X |