Nonlinear Volterra delay evolution inclusions subjected to nonlocal initial conditions
Copyright policy )Nonlinear Volterra delay evolution inclusions subjected to nonlocal initial conditions
This paper deals with a nonlinear Volterra delay evolution inclusion subjected to a nonlocal implicit initial condition. The evolution inclusion involves an $m$-dissipative operator (possibly multivalued and/or nonlinear) and a noncompact interval. We first consider the evolution inclusion subjected to a local initial condition and prove an existence result for bounded $C^0$-solutions. Then, using a fixed point theorem for upper semicontinuous multifunctions with contractible values, we obtain a global solvability result for the original problem. Finally, we present an example to illustrate the abstract result.
Evolution inclusions, Volterra integral equations, Applications of operator theory to differential and integral equations, equicontinuous semigroup, global solvability, Volterra delay evolution inclusion, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, \(C^0\)-solutions, nonlocal implicit initial condition
Evolution inclusions, Volterra integral equations, Applications of operator theory to differential and integral equations, equicontinuous semigroup, global solvability, Volterra delay evolution inclusion, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, \(C^0\)-solutions, nonlocal implicit initial condition
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).5 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!