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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Existence results for asymptotic linear Hammerstain integral equations via Morse Theory

100%
O’Regan D.
Commentationes Mathematicae
|
2009
|
tom 49
|
nr 1
EN
In this paper we establish some results for asymptotic linear Hammerstein integral equations. Using Morse theory and in particular critical groups we prove a number of existence results.
2
Content available remote

Weak and strong topologies and integral equations in Banach spaces

100%
O'Regan D.
Annales Polonici Mathematici
|
1995
|
tom 61
|
nr 3
245-260
EN
The Schauder-Tikhonov theorem in locally convex topological spaces and an extension of Krasnosel'skiĭ's fixed point theorem due to Nashed and Wong are used to establish existence of $L^α$ and C solutions to Volterra and Hammerstein integral equations in Banach spaces.
3
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Content available

Lefschetz Fixed Point Theorems for Approximative Type Maps in Fréchet Spaces

100%
O’Regan D.
Commentationes Mathematicae
|
2007
|
tom 47
|
nr 1
EN
In this paper using the projective limit approach we present new Lefschetz fixed point theorems for approximable type maps defined on PRANR’s.
4

Fixed point theory for multimaps defined on closed subsets of Fréchet spaces: the projective limit approach

64%
Agarwal R. P., O’Regan D.
Commentationes Mathematicae
|
2006
|
tom 46
|
nr 2
EN
New fixed point results are presented for maps defined on closed subsets of a Fréchet space \(E\). The proof relies on fixed point results in Banach spaces and viewing \(E\) as the projective limit of a sequence of Banach spaces.
5
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Weakly sequentially continuous maps and existence principles for elliptic equations

64%
Agarwal R., O'Regan D.
Applicationes Mathematicae
|
2003
|
tom 30
|
nr 4
451-460
EN
We present a Furi-Pera type theorem for weakly sequentially continuous maps. As an application we establish new existence principles for elliptic Dirichlet problems.
6
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Existence theory for single and multiple solutions to singular positone boundary value problems for the delay one-dimensional p-Laplacian

51%
Jiang D., Xu X., O'Regan D., Agarwal R.
Annales Polonici Mathematici
|
2003
|
tom 81
|
nr 3
237-259
EN
The existence of single and multiple nonnegative solutions for singular positone boundary value problems to the delay one-dimensional p-Laplacian is discussed. Throughout our nonlinearity f(·,y) may be singular at y = 0.
7
Content available remote

Positive and maximal positive solutions of singular mixed boundary value problem

51%
Agarwal R., O’Regan D., Staněk S.
Open Mathematics
|
2009
|
tom 7
|
nr 4
694-716
EN
The paper is concerned with existence results for positive solutions and maximal positive solutions of singular mixed boundary value problems. Nonlinearities h(t;x;y) in differential equations admit a time singularity at t=0 and/or at t=T and a strong singularity at x=0.
8
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Periodicity, almost periodicity for time scales and related functions

51%
Wang C., Agarwal R. P., O’Regan D.
Nonautonomous Dynamical Systems
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2016
|
tom 3
|
nr 1
24-41
EN
In this paper, we study almost periodic and changing-periodic time scales considered byWang and Agarwal in 2015. Some improvements of almost periodic time scales are made. Furthermore, we introduce a new concept of periodic time scales in which the invariance for a time scale is dependent on an translation direction. Also some new results on periodic and changing-periodic time scales are presented.
9
Content available remote

Multiplicity of positive solutions to second order differential equations with Neumann boundary conditions

51%
Chu J., Jiang D., O'Regan D., Agarwal R.
Applicationes Mathematicae
|
2005
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tom 32
|
nr 3
293-303
EN
We study the existence of positive solutions to second order nonlinear differential equations with Neumann boundary conditions. The proof relies on a fixed point theorem in cones, and the positivity of Green's function plays a crucial role in our study.
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