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Nonlocal elliptic problems

Andrzej Krzywicki, Tadeusz Nadzieja (2000)

Banach Center Publications

Some conditions for the existence and uniqueness of solutions of the nonlocal elliptic problem , are given.

Nonlocal systems of BVPs with asymptotically superlinear boundary conditions

Christopher S. Goodrich (2012)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider a coupled system of second-order boundary value problems with nonlocal, nonlinear boundary conditions, and we examine conditions under which such problems will have at least one positive solution. By imposing only an asymptotic growth condition on the nonlinear boundary functions, we are able to achieve generalizations over existing works and, in particular, we allow for the nonlocal terms to be able to be realized as Lebesgue-Stieltjes integrals possessing signed Borel...

Non-self mappings in modular spaces and common fixed point theorems

Abdolrahman Razani, Valdimir Rakočević, Zahraa Goodarzi (2010)

Open Mathematics

The aim of this paper, is to introduce the convex structure (specially, Takahashi convex structure) on modular spaces. Moreover, we are interested in proving some common fixed point theorems for non-self mappings in modular space.

Note on weakly inward mappings

Michal Fečkan (1996)

Annales Polonici Mathematici

The Nielsen fixed point theory is used to show several results for certain operator equations involving weakly inward mappings.

On a boundary value problem on the half-line for nonlinear two-dimensional delay differential systems

Ch. G. Philos (2007)

Annales Polonici Mathematici

This article is concerned with a boundary value problem on the half-line for nonlinear two-dimensional delay differential systems. By the use of the Schauder-Tikhonov theorem, a result on the existence of solutions is obtained. Also, via the Banach contraction principle, another result concerning the existence and uniqueness of solutions is established. Moreover, these results are applied to the special case of ordinary differential systems and to a certain class of delay differential systems. Furthermore,...

On a class of discontinuous operators in Hilbert spaces

Sebastiano Boscarino (2003)

Commentationes Mathematicae Universitatis Carolinae

We construct a class of discontinuous operators in infinite-dimensional separable Hilbert spaces, answering a natural question which arises in comparing a fixed point theorem of Altman and Shinbrot ([1], [4]) with its improvement obtained by Ricceri ([2], [3]).

On a fixed point theorem for weakly sequentially continuous mapping

Ireneusz Kubiaczyk (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Let E be a metrizable locally convex topological vector space x ∈ E, and let D be a closed convex subset of E such that x ∈ D. In this paper we prove that the weakly sequentially continuous mapping F: D ∪ D which satisfies V̅ = c̅o̅n̅v̅({x} ∪ F(V))⇒ V is relatively weakly compact, has a fixed point. Employing the above results we prove the existence theorem for the Cauchy problem x'(t) = f(t,x(t)), x(0) = x₀. As compared with the previous...

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