Existence results for functional and neutral functional integrodifferential inclusions with lower semicontinuous right-hand side.
The authors study the following initial value problems for functional integro-differential inclusions: (1) \(y'(t)\in F( t,y_t, \int_0^t k(t,s,y_s)\,ds)\), a.e. \(t\in [0,T]\), \(y(t)= \varphi(t)\), \(t\in [-r,0]\); (2) \(y''(t)\in F( t,y_t, \int_0^t k(t,s,y_s)\,dx)\), a.e. \(t\in [0,T]\), \(y(t)= \varphi(t)\), \(t\in [-r,0]\), \(y'(0)= \eta\) (3) \(\frac{d}{dt} [y(t)-g(t,y_t)]\in F( t,y_t, \int_0^t k(t,s,y_s)\,ds)\), a.e. \(t\in [0,T]\), \(y(t)= \varphi(t)\), \(t\in [-r,0]\), (4) \(\frac{d}{dt} [y'(t)- g(t,y_t)]\in F( t,y_t, \int_0^t k(t,s,y_s)\,ds)\) , a.e. \(t\in [0,T]\), \(y(t)= \varphi(t)\), \(t\in [-r,0]\), \(y'(0)= \eta\). By means of suitable fixed point theorems existence results are obtained.
functional integrodifferential inclusions
scientific article; zbMATH DE number 1956879
scientific article