We discuss the existence results of the parabolic evolution equation d(x(t)+g(t,x(t)))/dt+A(t)x(t)=f(t,x(t)) in Banach spaces, where A(t) generates an evolution system and functions f,g are continuous. We get the theo...We discuss the existence results of the parabolic evolution equation d(x(t)+g(t,x(t)))/dt+A(t)x(t)=f(t,x(t)) in Banach spaces, where A(t) generates an evolution system and functions f,g are continuous. We get the theorem of existence of a mild solution, the theorem of existence and uniqueness of a mild solution and the theorem of existence and uniqueness of an S-classical (semi-classical) solution. We extend the cases when g(t)=0 or A(t)=A.展开更多
文摘We discuss the existence results of the parabolic evolution equation d(x(t)+g(t,x(t)))/dt+A(t)x(t)=f(t,x(t)) in Banach spaces, where A(t) generates an evolution system and functions f,g are continuous. We get the theorem of existence of a mild solution, the theorem of existence and uniqueness of a mild solution and the theorem of existence and uniqueness of an S-classical (semi-classical) solution. We extend the cases when g(t)=0 or A(t)=A.