Open AccessExistence results for second order linear differential equations in Banach spaces
Author(s) -
M. Mursaleen,
Syed M. H. Rizvi
Publication year - 2018
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm160902015m
Subject(s) - mathematics , banach space , c0 semigroup , order (exchange) , differential equation , fixed point theorem , mathematical analysis , ordinary differential equation , picard–lindelöf theorem , linear differential equation , space (punctuation) , finance , economics , linguistics , philosophy
In this paper we are concerned with the existence of solutions for certain classes of second order differential equations. First we deal with an infinite system of second order linear differential equations, which is reduced to an ordinary differential equation posed in the space of convergent sequences. Next we investigate the problem of existence for a second order differential equation posed on an arbitrary Banach space. The used approach is based on the measures of noncompactness concept, the use of Darbo's fixed point theorem and Kamke comparison functions.