A class of linear partial neutral functional differential equations with nondense domain
The paper deals with the linear neutral differential equations on a Banach space \(X\), \[ {d\over dt} (x(t)- Bx(t- h))= A_0x(t)+ Cx(t- h)+ L(x_t),\quad t\geq 0,\quad x(0)= \varphi\in C_X, \] where \(A_0: D(A_0)\subseteq X\mapsto X\) is a linear operator, \(B,C\in{\mathcal L}(X)\), \(L\) is a continuous linear functional from \(C_X:= C([-h,0],X)\) into \(X, \varphi\in C_X\) and \(x_t(\theta)= x(t+ \theta)\), \({-h\leq\theta\leq 0}\). A variation-of-constants formula is derived allowing transformation of integral solutions of the above problem to solutions of an abstract Volterra integral equation. The authors prove existence and uniqueness results and show that the solutions generate an integrated semigroup.
neutral partial functional differential equations
scientific article; zbMATH DE number 1212347
scientific article