Teresa Winiarska

The aim of the paper is to prove two theorems on continuous dependence of mild solutions,
on initial nonlocal data, of the nonlocal Cauchy problems. For this purpose, the method
of semigroups and the theory of cosine family in Banach spaces are applied. The paper is based
on publications [1–5].

The aim of this paper is to prove the existence and uniqueness of solutions of the Dirichlet nonlocal problem with nonlocal initial condition. The considerations are extensions of results by E. Andreu-Vaillo, J. M. Mazón, J. D. Rossi and J. J. Toledo-Melero [1].

The aim of this paper is to give two theorems on the existence and uniqueness of mild and classical solutions of a nonlocal semilinear integro-differential evolution Cauchy problem for the first order equation. The method of semigroups, the Banach fixed-point theorem and the Bochenek theorem are applied to prove the existence and uniqueness of the solutions of the considered problem.

The aim of this paper is to prove two theorems on the existence and uniqueness of mild and classical solutions of a nonlocal semilinear functional-differential evolution Cauchy problem in a Banach space. The method of semigroups, the Banach fixed-point theorem and the Bochenek theorem (see [3]) about the existence and uniqueness of the classical solution of the first order differential evolution problem in a not necessarily reflexive Banach space are used to prove the existence and uniqueness of the solutions of the considered problem. The results are based on publications [1 — 8].

The aim of the paper is to prove theorems about the existence and uniqueness of mild
and classical solutions of a nonlocal semilinear functional-differential evolution Cauchy
problem. The method of semigroups, the Banach fixed-point theorem and theorems (see [2])
about the existence and uniqueness of the classical solutions of the first-order differential
evolution problems in a not necessarily reflexive Banach space are used to prove the existence
and uniqueness of the solutions of the problems considered. The results obtained are based
on publications [1–6].