We prove existence and uniqueness of classical solutions for an incomplete second-order abstract Cauchy problem associated with operators which have polynomially bounded resolvent. Some examples of differential operators to which our abstract result applies are also included.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm155-2-7, author = {F. Periago and B. Straub}, title = {On the existence and uniqueness of solutions for an incomplete second-order abstract Cauchy problem}, journal = {Studia Mathematica}, volume = {157}, year = {2003}, pages = {183-193}, zbl = {1054.34093}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm155-2-7} }
F. Periago; B. Straub. On the existence and uniqueness of solutions for an incomplete second-order abstract Cauchy problem. Studia Mathematica, Tome 157 (2003) pp. 183-193. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm155-2-7/