scholarly journals Topological structure of solution sets to parabolic problems

2005 ◽  
Vol 25 (2) ◽  
pp. 313
Author(s):  
Vladimír Ďurikovič ◽  
Monika Ďurikovičová
Keyword(s):  
Topological Structure ◽  
Parabolic Problems ◽  
Solution Sets

scholarly journals Some New Results for the Sobolev-Type Fractional Order Delay Systems with Noncompact Semigroup

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Qiaomin Xiang ◽  
Pengxian Zhu
Keyword(s):  
Fractional Order ◽  
Topological Structure ◽  
Existence Result ◽  
Delay Systems ◽  
Sobolev Type ◽  
Multivalued Maps ◽  
Solution Sets ◽  
Mild Conditions ◽  
Partial Differential Inclusions ◽  
Fixed Point Principle

The topological structure of solution sets for the Sobolev-type fractional order delay systems with noncompact semigroup is studied. Based on a fixed point principle for multivalued maps, the existence result is obtained under certain mild conditions. With the help of multivalued analysis tools, the compactness of the solution set is also obtained. Finally, we apply the obtained abstract results to the partial differential inclusions.

1407 A Topological Structure Design Method for Multi-Objective Satisfactory Design Solution Sets

2013 ◽  
Vol 2013.23 (0) ◽  
pp. _1407-1_-_1407-8_
Author(s):  
Masato INOUE ◽  
Daisuke ASADA ◽  
Nobuhito KATO ◽  
Nobuyoshi ISHIBAI ◽  
Haruo ISHIKAWS
Keyword(s):  
Topological Structure ◽  
Design Method ◽  
Structure Design ◽  
Design Solution ◽  
Solution Sets ◽  
Multi Objective

scholarly journals A note on continuation problems

1986 ◽  
Vol 28 (1) ◽  
pp. 55-61 ◽  
Author(s):  
Rita Nugari
Keyword(s):  
Banach Spaces ◽  
Topological Structure ◽  
Vector Fields ◽  
Existence Of Solution ◽  
Index Zero ◽  
Bounded Linear ◽  
Solution Sets ◽  
Connected Sets ◽  
Continuation Principle ◽  
Parameter Dependent

Recently M. Martelli [6] and M. Furi and M. P. Pera [1] proved some interesting results about the existence and the global topological structure of connected sets of solutions to problems of the form:Lx = N(λ, x)with L:E → F a bounded linear Fredholm operator of index zero (where E, F are real Banach spaces), and N:ℝ × E → F a nonlinear map satisfying suitable conditions.While the existence of solution sets for this kind of problem follows from the Leray–Schauder continuation principle, it is our aim to show in this note that their global topological structure can be obtained as a consequence of the theory developed by J. Ize, I. Massabò, J. Pejsachowicz and A. Vignoli in [3, 4] about parameter dependent compact vector fields in Banach spaces.

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