Continuous dependence of mild solutions, on initial nonlocal data, of the nonlocal evolution Cauchy problems

Ludwik Byszewski,

Teresa Winiarska

Abstrakt

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].

Słowa kluczowe: evolution Cauchy problems, continuous dependence of solutions, nonlocal conditions
References

Byszewski L., Existence and uniqueness of mild and classical solutions of semilinear functional-differential evolution nonlocal Cauchy problem, Sellected Problems of Mathematics, Cracow University of Technology, Anniversary Issue 6, 1995, 25-33.

Byszewski L., Winiarska T., An abstract nonlocal second order evolution problem, Opuscula Mathematica, 32.1, 2012, 75-82.

Pazy A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer–Verlag, New York, Berlin, Heidelberg, Tokyo 1983.

Szarski J., Differential Inequalities, Polish Scientific Publishers, Warszawa 1967.

Winiarska T., Differential Equations with Parameters, Monograph 68, Technical University of Cracow, Cracow 1988.