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In this paper, assuming a natural sequentially compact conditionwe establish new fixed point theorems for Urysohn type maps between Fréchet spaces. In Section 2 we present new LeraySchauder alternatives, Krasnoselskii and Lefschetz fixed point theory for admissible type maps. The proofs rely on fixed point theory in Banach spaces and viewing a Fréchet space… (More)

In this paper, we present fixed point results for generalized contractions defined on a complete gauge space E. Also, we consider families of generalized contractions {ft : X → E}t∈[0,1] where X ⊂ E is closed and can have empty interior. We give conditions under which the existence of a fixed point for some ft0 imply the existence of a fixed point for every… (More)

This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The investigation is performed via fixed point theory in a complete metric space by defining appropriate nonexpansive or… (More)

We use strongly pseudocontraction to regularize the following ill-posed monotone variational inequality: finding a point x∗ with the property x∗ ∈ Fix T such that 〈 I − S x∗, x − x∗〉 ≥ 0, x ∈ Fix T where S, T are two pseudocontractive self-mappings of a closed convex subset C of a Hilbert space with the set of fixed points Fix T / ∅. Assume the solution… (More)

- Marlène Frigon
- 2001

In this paper, we introduce a new notion of linking which includes in particular the notions of homotopical linking and local linking. Critical point theorems for continuous functionals on metric spaces are presented. Finally, an application to nonlinear elliptic problems at resonance is given. 1991 Mathematics Subject Classification. Primary 58E05;… (More)

In 1929, Knaster et al. 1 had proved the well-known KKM theorem on n-simplex. Besides, in 1961, Fan 2 had generalized the KKM theorem to an infinite dimensional topological vector space. Later, Amini et al. 3 had introduced the class of KKM-typemappings onmetric spaces and established some fixed point theorems for this class. In this paper, we define a… (More)

- Marlène Frigon, Donal O'Regan
- Fuzzy Sets and Systems
- 2002

- Marlène Frigon, H. Gilbert
- 2011

and Applied Analysis 3 In the last section of this paper,we study the system 1.2 . Again, we introduce a notion of solution-tube of 1.2 which generalizes the notion of lower and upper solutions used by Atici et al. 8 . This notion generalizes also condition 1.5 and the notion of solution-tube of systems of second-order differential equations introduced in… (More)

We establish the existence of a nontrivial solution to systems of coupled Poisson equations with critical growth in unbounded domains. The proofs rely on a generalized linking theorem due to Krysewski and Szulkin [9], and on a concentration-compactness argument since the Palais-Smale condition fails at all critical levels. Mathematical Subject… (More)