Back to Search
Start Over
Perturbed evolution problems with absolutely continuous variation in time and applications.
- Source :
- Journal of Fixed Point Theory & Applications; Jun2019, Vol. 21 Issue 2, pN.PAG-N.PAG, 1p
- Publication Year :
- 2019
-
Abstract
- This paper is devoted to the existence and uniqueness of absolutely continuous solutions in evolution problems of the form - d u d t (t) ∈ A (t) u (t) + f (t , u (t)) in a new setting. For each t, A (t) : D (A (t)) → 2 H is a maximal monotone operator in a Hilbert space H and the perturbation f is separately integrable on [0, T] and separately Lipschitz on H. It is assumed that t ↦ A (t) has absolutely continuous variation, in the sense of Vladimirov's pseudo-distance. Some extensions are also provided allowing new applications of our results to a larger number of problems modeled by maximal monotone operators. In particular, we solve evolution problems with multivalued upper semicontinuous perturbations, by using a fixed point theorem. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16617738
- Volume :
- 21
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Journal of Fixed Point Theory & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 135963033
- Full Text :
- https://doi.org/10.1007/s11784-019-0666-2