Geodesic
A survey and some new results on the existence of solutions of IPBVPs for first order functional differential equations
Applications of Mathematics, Tome 54 (2009) no. 6, pp. 527-549

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This paper deals with the periodic boundary value problem for nonlinear impulsive functional differential equation $$ \begin{cases} x'(t)=f(t,x(t),x(\alpha _1(t)),\cdots ,x(\alpha _n(t))) \text {for a.e.} \ t\in [0,T], \Delta x(t_k)=I_k(x(t_k)), \ k=1,\cdots ,m, x(0)=x(T). \end{cases} $$ We first present a survey and then obtain new sufficient conditions for the existence of at least one solution by using Mawhin's continuation theorem. Examples are presented to illustrate the main results.
This paper deals with the periodic boundary value problem for nonlinear impulsive functional differential equation $$ \begin{cases} x'(t)=f(t,x(t),x(\alpha _1(t)),\cdots ,x(\alpha _n(t))) \text {for a.e.} \ t\in [0,T], \Delta x(t_k)=I_k(x(t_k)), \ k=1,\cdots ,m, x(0)=x(T). \end{cases} $$ We first present a survey and then obtain new sufficient conditions for the existence of at least one solution by using Mawhin's continuation theorem. Examples are presented to illustrate the main results.
DOI : 10.1007/s10492-009-0032-6
Classification : 34B10, 34B15, 34K10, 34K45, 47N20
Keywords: periodic boundary value problem; impulsive differential equation; fixed-point theorem; growth condition 
Liu, Yuji. A survey and some new results on the existence of solutions of IPBVPs for first order functional differential equations. Applications of Mathematics, Tome 54 (2009) no. 6, pp. 527-549. doi: 10.1007/s10492-009-0032-6
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     title = {A survey and some new results on the existence of solutions of {IPBVPs} for first order functional differential equations},
     journal = {Applications of Mathematics},
     pages = {527--549},
     year = {2009},
     volume = {54},
     number = {6},
     doi = {10.1007/s10492-009-0032-6},
     mrnumber = {2563123},
     zbl = {1212.34184},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-009-0032-6/}
}
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