Opuscula Math. 32, no. 1 (2012), 75-82
http://dx.doi.org/10.7494/OpMath.2012.32.1.75
Opuscula Mathematica
An abstract nonlocal second order evolution problem
Ludwik Byszewski
Teresa Winiarska
Abstract. The aim of the paper is to prove theorems on the existence and uniqueness of mild and classical solutions of a semilinear evolution second order equation together with nonlocal conditions. The theory of strongly continuous cosine families of linear operators in a Banach space is applied.
Keywords: nonlocal, second order, evolution problem, Banach space.
Mathematics Subject Classification: 34K30, 34K99.
- Ludwik Byszewski
- Krakow University of Technology, Institute of Mathematics, ul. Warszawska 24, 31-155 Krakow, Poland
- Teresa Winiarska
- Krakow University of Technology, Institute of Mathematics, ul. Warszawska 24, 31-155 Krakow, Poland
- Received: 2010-12-02.
- Revised: 2011-03-10.
- Accepted: 2011-03-10.
