Local and global existence and uniqueness of solution for abstract differential equations with state-dependent argument. (English) Zbl 1523.34086
The paper is concerned with the existence and uniqueness of a non-Lipschitz solution for an abstract ordinary differential equations with state-dependent argument. In addition, to prove their results, the authors made some \(L^p\)-Lipschitz assumptions. They also study the local and global existence and uniqueness of solution and the existence of solution for a particular case.
Reviewer: Mustapha Yebdri (Tlemcen)
MSC:
| 34K43 | Functional-differential equations with state-dependent arguments |
| 34K30 | Functional-differential equations in abstract spaces |
| 47D06 | One-parameter semigroups and linear evolution equations |
Keywords:
abstract ordinary differential equations; state-dependent argument; local solution; global solution; uniqueness of solution; mild solution; classical solution; strict solutionReferences:
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