ON WELL POSEDNESS OF ABSTRACT NONLINEAR FUNCTIONAL SECOND ORDER INTEGRO-DIFFERENTIAL EQUATION WITH NONLOCAL CONDITION
RUPALI S. JAIN *
School of Mathematical Sciences, Swami Ramanand Teerth Marathwada University, Nanded-431 606, Maharashtra, India.
*Author to whom correspondence should be addressed.
The present paper deals with well-posedness of initial value problem for second order nonlinear functional integro-differential equations with nonlocal condition in Banach spaces. We use modified version of Banach contraction theorem and Pachpatte's inequality to establish our results.
Keywords: Well-posedness, functional, integro-dierential equation, fixed point, nonlocal, pachpatte's inequality