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Hindawi Publishing Corporation
International Journal of Mathematics and Mathematical Sciences
RAVI P. AGARWAL
JEWGENI H. DSHALALOW
**DONAL** **O'REGAN**
New Leray-Schauder alternatives are presented for Mo ... : Department of Mathematical Sciences, College of Science, Florida Institute of Technology, Melbourne, FL 32901 -6975, USA E-mail address: **Donal** **O'Regan** : Department of Mathematics, National University of

We introduce a class of functions called geodesic -preinvex and geodesic -invex functions on Riemannian manifolds and generalize the notions to the so-called geodesic quasi/pseudo -preinvex and geodesic quasi/pseudo -invex functions. We discuss the links among these functions under appropriate conditions and obtain results concerning extremum points of a nonsmooth geodesic...

By using bifurcation techniques, this paper investigates the existence of nodal solutions for a class of fourth-order -point boundary value problems. Our results improve those in the literature.

Hindawi Publishing Corporation
Journal of Applied Mathematics and Stochastic Analysis
Volume 2006
MULTIVALUED H -ESSENTIAL MAPS OF ACYCLIC TYPE ON HAUSDORFF TOPOLOGICAL SPACES
**DONAL** **O'REGAN**
This

We present new Leray-Schauder alternatives, Krasnoselskii and Lefschetz fixed point theory for multivalued maps between Fréchet spaces. As an application we show that our results are directly applicable to establish the existence of integral equations over infinite intervals.

The boundary value problems for degenerate anisotropic differential operator equations with variable coefficients are studied. Several conditions for the separability and Fredholmness in Banach-valued spaces are given. Sharp estimates for resolvent, discreetness of spectrum, and completeness of root elements of the corresponding differential operators are obtained. In the last...

We investigate the existence of positive solutions of singular problem , , , . Here, and the Carathéodory function may be singular in all its space variables . The results are proved by regularization and sequential techniques. In limit processes, the Vitali convergence theorem is used.

We present new fixed point theorems for ws-compact operators. Our fixed point results are obtained under Sadovskii, Leray-Schauder, Rothe, Altman, Petryshyn, and Furi-Pera type conditions. An example is given to show the usefulness and the applicability of our results.

We present some fixed point theorems for the sum of a weakly-strongly continuous map and a nonexpansive map on a Banach space . Our results cover several earlier works by Edmunds, Reinermann, Singh, and others.

Hindawi Publishing Corporation
Fixed Point Theory and Applications
FIXED POINT THEORY ON EXTENSION-TYPE SPACES AND ESSENTIAL MAPS ON TOPOLOGICAL SPACES
**DONAL** **O'REGAN** 0
0 **Donal** **O'Regan**: Department

In this article, we consider the following systems of Fredholm integral equations: u i ( t ) = h i ( t ) + ∫ 0 T g i ( t , s ) f i ( s , u 1 ( s ) , u 2 ( s ) , … , u n ( s ) ) d s , t ∈ [ 0 , T ] , 1 ≤ i ≤ n , u i ( t ) = h i ( t ) + ∫ 0 ∞ g i ( t , s ) f i ( s , u 1 ( s ) , u 2 ( s ) , … , u n ( s ) ) d s , t ∈ [ 0 , ∞ ) , 1 ≤ i ≤ n . Using an argument originating from Brezis...

In this article, we consider the following systems of Fredholm integral equations: u i ( t ) = h i ( t ) + ∫ 0 T g i ( t , s ) f i ( s , u 1 ( s ) , u 2 ( s ) , … , u n ( s ) ) d s , t ∈ [ 0 , T ] , 1 ≤ i ≤ n , u i ( t ) = h i ( t ) + ∫ 0 ∞ g i ( t , s ) f i ( s , u 1 ( s ) , u 2 ( s ) , … , u n ( s ) ) d s , t ∈ [ 0 , ∞ ) , 1 ≤ i ≤ n . Using an argument originating from Brezis...

This paper studies the eigenvalue interval for the singular boundary value problem , where may be singular at , , and may change sign and be superlinear at . The approach is based on an approximation method together with the theory of upper and lower solutions.

**O'REGAN** 0
0 **Donal** **O'Regan**: Department of Mathematics, National University of Ireland , Galway, University Road, Galway , Ireland E-mail address:
We study the existence and multiplicity of solutions for ... Hindawi Publishing Corporation
Journal of Inequalities and Applications
Volume 2006
EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR SOME THREE-POINT NONLINEAR BOUNDARY VALUE PROBLEMS
XU XIAN 0
**DONAL**

We present new existence results for singular discrete initial and boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign.

Some multiplicity results for solutions of an impulsive boundary value problem are obtained under the condition of non-well-ordered upper and lower solutions. The main ideas of this paper are to associate a Leray-Schauder degree with the lower or upper solution.

The paper discusses the existence of positive solutions, dead core solutions, and pseudo dead core solutions of the singular problem , , . Here is a positive parameter, , , , may be singular at and is singular at .

**O'Regan**: Department of Mathematics, National University of Ireland , Galway , Ireland
1 Johnny Henderson: Department of Mathematics, Baylor University , Waco, TX 76798 , USA
2 Richard Avery: College of Arts