33 papers found.

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Journal of Applied Mathematics and Stochastic Analysis
VOLTERRA AND URYSOHN INTEGRAL EQUATIONS IN BANACH SPACES
0 **DONAL** **O'REGAN** University College Galway, Department
We use topological methods to

Journal of Applied Mathematics and Stochastic Analysis
VOLTERRA AND URYSOHN INTEGRAL EQUATIONS IN BANACH SPACES
0 **DONAL** **O'REGAN** University College Galway, Department
We use topological methods to

This paper presents an upper and lower solution theory for boundary value problems modelled from the Thomas–Fermi equation subject to a boundary condition corresponding to the neutral atom with Bohr radius.

Hindawi Publishing Corporation
Journal of Applied Mathematics and Stochastic Analysis
0 **Donal** **O'Regan**: Department of Mathematics, National University of Ireland , Galway , Ireland E-mail address

This paper presents an upper and lower solution theory for boundary value problems modelled from the Thomas–Fermi equation subject to a boundary condition corresponding to the neutral atom with Bohr radius.

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

Hindawi Publishing Corporation
Journal of Applied Mathematics and Stochastic Analysis
RAVI P. AGARWAL 0
**DONAL** **O'REGAN** 0
OLEKSANDR E. ZERNOV 0
0 **Donal** **O'Regan**: Department of Mathematics, National

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...

We prove Krasnosel'skii type fixed point theorems in situations where the domain is not necessarily convex. As an application, the existence of solutions for perturbed integral equation is considered in p-normed spaces.

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...

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 . Open image in new window Using an argument...

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...

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.

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.

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.

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.

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.