TY - JOUR
AU - WU, JIANHONG
PY - 1991/03/01
Y2 - 2022/10/05
TI - UNIFIED TREATMENT OF LOCAL THEORY OF NFDES WITH INFINITE DELAY
JF - Tamkang Journal of Mathematics
JA - Tamkang J. Math.
VL - 22
IS - 1
SE - Papers
DO - 10.5556/j.tkjm.22.1991.4569
UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/4569
SP - 51-72
AB - <div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span style="font-size: 9.000000pt; font-family: 'TimesNewRomanPSMT';">The present paper gives a unified treatment of the local theory of NFDEs with infinite delay on a class of comparatively comprehensive phase spaces which contain admissible phase spaces and </span><span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPS'; font-style: italic;">BC </span><span style="font-size: 9.000000pt; font-family: 'TimesNewRomanPSMT';">space as special cases. Condi- tions and assumptions are imposed on two functionals defining the equation, and therefore independent of the structure and properties of phase spaces. This al- lows us to determine phase spaces and sufficient conditions guaranteeing existence and uniqueness of solutions according to the property of the equation at hand as opposed to preassign a phase space to dictate the conditions. </span><span style="font-size: 10.000000pt; font-family: 'TimesNewRomanPSMT';">An </span><span style="font-size: 9.000000pt; font-family: 'TimesNewRomanPSMT';">example will be given to show how to choose the phase space according to the fading memory characteristic of Volterra integrodifferential equations so that the Cauchy initial value problem is well posed. </span></p></div></div></div>
ER -