Solvability of (k,n-k) Conjugate Boundary Value Problems with Integral Boundary Conditions at Resonance
We investigate a (k,n-k) conjugate boundary value problem with integral boundary conditions. By using Mawhin continuation theorem, we study the solvability of this boundary value problem at resonance. It is shown that the boundary value problem (-1)n-kφ(n)(x)=fx,φx,φ′x,…,φ(n-1)(x), x∈[0,1], φ(i)(0)=...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/3454879 |
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doaj-7ea8b8fa0fd84e9097004972cb2179112020-11-24T22:27:28ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/34548793454879Solvability of (k,n-k) Conjugate Boundary Value Problems with Integral Boundary Conditions at ResonanceQiao Sun0Yujun Cui1Department of Mathematics, Shandong University of Science and Technology, Qingdao 266590, ChinaState Key Laboratory of Mining Disaster Prevention and Control Co-Founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, ChinaWe investigate a (k,n-k) conjugate boundary value problem with integral boundary conditions. By using Mawhin continuation theorem, we study the solvability of this boundary value problem at resonance. It is shown that the boundary value problem (-1)n-kφ(n)(x)=fx,φx,φ′x,…,φ(n-1)(x), x∈[0,1], φ(i)(0)=φ(j)(1)=0, 1≤i≤k-1, 0≤j≤n-k-1, φ(0)=∫01φ(x)dA(x) has at least one solution under some suitable conditions.http://dx.doi.org/10.1155/2016/3454879 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Qiao Sun Yujun Cui |
| spellingShingle |
Qiao Sun Yujun Cui Solvability of (k,n-k) Conjugate Boundary Value Problems with Integral Boundary Conditions at Resonance Journal of Function Spaces |
| author_facet |
Qiao Sun Yujun Cui |
| author_sort |
Qiao Sun |
| title |
Solvability of (k,n-k) Conjugate Boundary Value Problems with Integral Boundary Conditions at Resonance |
| title_short |
Solvability of (k,n-k) Conjugate Boundary Value Problems with Integral Boundary Conditions at Resonance |
| title_full |
Solvability of (k,n-k) Conjugate Boundary Value Problems with Integral Boundary Conditions at Resonance |
| title_fullStr |
Solvability of (k,n-k) Conjugate Boundary Value Problems with Integral Boundary Conditions at Resonance |
| title_full_unstemmed |
Solvability of (k,n-k) Conjugate Boundary Value Problems with Integral Boundary Conditions at Resonance |
| title_sort |
solvability of (k,n-k) conjugate boundary value problems with integral boundary conditions at resonance |
| publisher |
Hindawi Limited |
| series |
Journal of Function Spaces |
| issn |
2314-8896 2314-8888 |
| publishDate |
2016-01-01 |
| description |
We investigate a (k,n-k) conjugate boundary value problem with integral boundary conditions. By using Mawhin continuation theorem, we study the solvability of this boundary value problem at resonance. It is shown that the boundary value problem (-1)n-kφ(n)(x)=fx,φx,φ′x,…,φ(n-1)(x), x∈[0,1], φ(i)(0)=φ(j)(1)=0, 1≤i≤k-1, 0≤j≤n-k-1, φ(0)=∫01φ(x)dA(x) has at least one solution under some suitable conditions. |
| url |
http://dx.doi.org/10.1155/2016/3454879 |
| work_keys_str_mv |
AT qiaosun solvabilityofknkconjugateboundaryvalueproblemswithintegralboundaryconditionsatresonance AT yujuncui solvabilityofknkconjugateboundaryvalueproblemswithintegralboundaryconditionsatresonance |
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1725749816630181888 |