On a class of second-order impulsive boundary value problem at resonance
We consider the following impulsive boundary value problem, x″(t)=f(t,x,x′), t∈J\{t1,t2,…,tk}, Δx(ti)=Ii(x(ti),x′(ti)), Δx′(ti)=Ji(x(ti),x′(ti)), i=1,2,…,k, x(0)=(0), x′(1)=∑j=1m−2αjx′(ηj). By using the coincidence degree theory, a general theorem concerning the problem is given. Moreover, we get a...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/62512 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832565396155138048 |
|---|---|
| author | Guolan Cai Zengji Du Weigao Ge |
| author_facet | Guolan Cai Zengji Du Weigao Ge |
| author_sort | Guolan Cai |
| collection | DOAJ |
| description | We consider the following impulsive boundary value problem,
x″(t)=f(t,x,x′), t∈J\{t1,t2,…,tk},
Δx(ti)=Ii(x(ti),x′(ti)), Δx′(ti)=Ji(x(ti),x′(ti)),
i=1,2,…,k, x(0)=(0),
x′(1)=∑j=1m−2αjx′(ηj). By using the
coincidence degree theory, a general theorem concerning the
problem is given. Moreover, we get a concrete existence result
which can be applied more conveniently than recent results. Our
results extend some work concerning the usual m-point boundary
value problem at resonance without impulses. |
| format | Article |
| id | doaj-art-8a3c3679c0dd49a9ae11fd64a40f905a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8a3c3679c0dd49a9ae11fd64a40f905a2025-02-03T01:07:50ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/6251262512On a class of second-order impulsive boundary value problem at resonanceGuolan Cai0Zengji Du1Weigao Ge2Department of Mathematics and Computer, Central University for Nationalities, Beijing 100081, ChinaDepartment of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, ChinaDepartment of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, ChinaWe consider the following impulsive boundary value problem, x″(t)=f(t,x,x′), t∈J\{t1,t2,…,tk}, Δx(ti)=Ii(x(ti),x′(ti)), Δx′(ti)=Ji(x(ti),x′(ti)), i=1,2,…,k, x(0)=(0), x′(1)=∑j=1m−2αjx′(ηj). By using the coincidence degree theory, a general theorem concerning the problem is given. Moreover, we get a concrete existence result which can be applied more conveniently than recent results. Our results extend some work concerning the usual m-point boundary value problem at resonance without impulses.http://dx.doi.org/10.1155/IJMMS/2006/62512 |
| spellingShingle | Guolan Cai Zengji Du Weigao Ge On a class of second-order impulsive boundary value problem at resonance International Journal of Mathematics and Mathematical Sciences |
| title | On a class of second-order impulsive boundary value
problem at resonance |
| title_full | On a class of second-order impulsive boundary value
problem at resonance |
| title_fullStr | On a class of second-order impulsive boundary value
problem at resonance |
| title_full_unstemmed | On a class of second-order impulsive boundary value
problem at resonance |
| title_short | On a class of second-order impulsive boundary value
problem at resonance |
| title_sort | on a class of second order impulsive boundary value problem at resonance |
| url | http://dx.doi.org/10.1155/IJMMS/2006/62512 |
| work_keys_str_mv | AT guolancai onaclassofsecondorderimpulsiveboundaryvalueproblematresonance AT zengjidu onaclassofsecondorderimpulsiveboundaryvalueproblematresonance AT weigaoge onaclassofsecondorderimpulsiveboundaryvalueproblematresonance |