Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces
Copyright policy )Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces
We prove two existence theorems for the integrodifferential equation of mixed type:x'(t)=f(t,x(t),∫0tk1(t,s)g(s,x(s))ds,∫0ak2(t,s)h(s,x(s))ds),x(0)=x0, where in the first part of this paperf, g, h, xare functions with values in a Banach spaceEand integrals are taken in the sense of Henstock-Kurzweil (HK). In the second partf, g, h, xare weakly-weakly sequentially continuous functions and integrals are taken in the sense of Henstock-Kurzweil-Pettis (HKP) integral. Additionally, the functionsf, g, h, xsatisfy some conditions expressed in terms of the measure of noncompactness or the measure of weak noncompactness.
- RK University India
- Adam Mickiewicz University in Poznań Poland
Other nonlinear integral equations, Integro-ordinary differential equations, Banach space, nonlinear integrodifferential equation, QA1-939, Henstock-Pettis integral, Abstract integral equations, integral equations in abstract spaces, Mathematics
Other nonlinear integral equations, Integro-ordinary differential equations, Banach space, nonlinear integrodifferential equation, QA1-939, Henstock-Pettis integral, Abstract integral equations, integral equations in abstract spaces, Mathematics
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