Abstract
In this paper we study the existence and uniqueness of mild andclassical solutions for a nonlinear impulsive integral evolutionequation $u'(t)= Au(t)+f(t,u(t),\int_0^tk(t,s)u(s)ds), t>0, t\ne t_i,$ $u(0)= u_0,$ $\Delta u(t_i)=I_i(u(t_i)). i= 1,2,....,p.$ in a Banach space X, where A is the infinitesimal generator of astrongly continuous semigroup,$ \Delta u(t_i)=u(t^+_i)-u(t^-_i)$and $I's$ are some operator. We apply the semigroup theory to studythe existence and uniqueness of the mild solutions, and then showthat the mild solution give rise to classical solution if $f$ iscontinuously differentiable.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.