Topological structure of solution sets to differential problems in Fréchet spaces (original) (raw)

Topological structure of solution sets: current results

2000

We shall present current results concerning Browder–Guptatype theorems, Banach principle for multivalued mappings and the inverse limit method including its applications to ordinary differential equations and differential inclusions. Consequently, Aronszajn’s-type topological characterization of the set of solutions for differential equations and inclusions is considered. Note that some new results of the above mentioned type will be discussed. AMS Subject Classification. 59B99, 54C60, 47H10, 54H25, 55M20, 34A60, 46A04, 55M25

Topological structure of solution sets for impulsive differential inclusions in Fr�chet spaces

Fuel and Energy Abstracts, 2011

In this paper, we consider the existence of solutions as well as the topological and geometric structure of solution sets for first-order impulsive differential inclusions in some Fréchet spaces. Both the initial and terminal problems are considered. Using ingredients from topology and homology, the topological structures of solution sets (closedness and compactness) as well as some geometric properties (contractibility, acyclicity, ARAR and RδRδ) are investigated. Some of our existence results are obtained via the method of taking the inverse system limit on noncompact intervals.

Fixed point theorems for maps on cones in Frechet spaces via the projective limit approach

2016

We present fixed point results for admissibly compact maps on cones in Fr´echet spaces. We first extend the Krasnosel’ski˘i fixed point theorem with order type cone-compression and cone-expansion conditions. Then, we extend the monotone iterative method to this context. Finally, we present fixed point results under a combination of the assumptions of the previous results. More precisely, we combine a cone-compressing or cone-extending condition only on one side of the boundary of an annulus with an assumption on the existence of an upper fixed point. In addition, we show that the usual monotonicity condition can be weaken