Positive Solutions for Neumann Boundary Value Problems of Second-Order Impulsive Differential Equations in Banach Spaces
The existence of positive solutions for Neumann boundary value problem of second-order impulsive differential equations −u″(t)+Mu(t)=f(t,u(t), t∈J, t≠tk, -Δu'|t=tk=Ik(u(tk)), k=1,2,…,m, u'(0)=u'(1)=θ, in an ordered Banach space E was discussed by employing the fixed point index theo...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/401923 |
| Summary: | The existence of positive solutions for Neumann boundary value problem of second-order impulsive differential equations −u″(t)+Mu(t)=f(t,u(t),
t∈J, t≠tk, -Δu'|t=tk=Ik(u(tk)), k=1,2,…,m, u'(0)=u'(1)=θ, in an ordered Banach space E was discussed by employing the fixed point index theory of condensing mapping, where M>0 is a constant, J=[0,1], f∈C(J×K,K), Ik∈C(K,K), k=1,2,…,m, and K is the cone of positive elements in E. Moreover, an application is given to illustrate the main result. |
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| ISSN: | 1085-3375 1687-0409 |