Lupulescu, Vasile Continuous selections of solution sets to second order evolution equations. (English) Zbl 1114.35312 Acta Univ. Apulensis, Math. Inform. 7, 163-170 (2004). Summary: We prove the existence of a continuous selection of the multivalued map \((\xi,\eta)\to A_F(\xi,\eta)\), where \(A_F(\xi,\eta)\) is the set of all mild solutions of the Cauchy problem \[ x''\in Ax+F(t,x),\;x(0)=\xi,\;x(0)=\eta \] assuming that \(F\) is Lipschitzian with respect to \(x\) and \(A\) is the infinitesimal generator of a strongly cosine family of linear operators on a Banach space \(E\). MSC: 35G25 Initial value problems for nonlinear higher-order PDEs 47D09 Operator sine and cosine functions and higher-order Cauchy problems Keywords:multifunctions; Cauchy problem; continuous selection; strongly cosine familty; mild solutions PDFBibTeX XMLCite \textit{V. Lupulescu}, Acta Univ. Apulensis, Math. Inform. 7, 163--170 (2004; Zbl 1114.35312) Full Text: EuDML