Complete abstract differential equations of elliptic type with general Robin boundary conditions, in UMD spaces
Let \(X\) be a UMD space. The authors consider the second order abstract differential equation \[ u''(x)+2Bu'(x)+Au(x)=f(x) \] for \( x\in (0,1)\), together with the abstract Robin boundary conditions: \[ u'(0)-Hu(0)=d_0; { } u(1)=u_1, \] where \(A\), \(B\) and \(H\) are linear operators on \(X\). Under various conditions on \(A\), \(B\) and \(H\), the authors prove the existence and uniqueness of the solution. As applications, two examples of partial differential equations are given to illustrate the results.
abstract differential equations of second order
scientific article; zbMATH DE number 5869365