Existence of solutions of nonlinear integrodifferential equations of sobolev type with nonlocal condition in Banach spaces

A Class of Nonlocal Impulsive Problems for Integrodifferential Equations in Banach Spaces

“…For the importance of nonlocal conditions in different fields, we refer the reader to [7][8][9][10] and the references contained therein. Especially, the integrodifferential equations with nonlocal conditions has been investigated by Balachandran, Liu and other researchers extensively (see [11][12][13][14]17,18,21]). …”

On fractional impulsive equations of Sobolev type with nonlocal condition in Banach spaces

“…The Sobolev type semilinear integrodifferential equation serves as an abstract formulation of partial integrodifferential equation which arise in various applications such as in the flow of fluid through fissured rocks [13], thermodynamics and shear in second order fluids and so on. Balachandran et al [14] established the existence of solutions for Sobolev type semilinear integrodifferential equation whereas Balachandran and Uchiyama [15] studied the existence of solutions of nonlinear integrodifferential equations of Sobolev type in Banach spaces. The problem of existence of solutions of evolution equations with nonlocal condition was initiated by Byszewski [16] and subsequently studied by several authors for different kinds of problems [17,18].…”

Existence of solutions to Sobolev‐type partial neutraldifferential equations

“…Brill [5] and Showalter [14,15] established the existence of solutions of semilinear evolution equations of Sobolev type in Banach spaces. On the other hand, Balachandran and Uchiyama [4] considered an integrodifferential equation of Sobolev type with a nonlocal condition and proved the existence of mild and strong solutions.…”