Existence of weak solutions for abstract hyperbolic-parabolic equations.
This paper presents existence results for initial and boundary value problems for nonlinear differential equations in Banach spaces.
This note is concerned with the existence of mild solutions defined on a compact real interval for first and second order semilinear functional differential inclusions.
Cauchy problem, boundary value problems with a boundary value condition and Sturm-Liouville problems related to the operator differential equation are studied for the general case, even when the algebraic equation is unsolvable. Explicit expressions for the solutions in terms of data problem are given and computable expressions of the solutions for the finite-dimensional case are made available.