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Fixed point theory for Mönch-type maps defined on closed subsets of Fréchet spaces: the projective limit approach

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

Multiplicity Results Using Bifurcation Techniques for a Class of Fourth-Order -Point Boundary Value Problems

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.

Fixed Point Theory for Admissible Type Maps with Applications

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.

Degenerate Anisotropic Differential Operators and Applications

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...

Positive Solutions of Singular Complementary Lidstone Boundary Value Problems

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.

Fixed Point Theorems for ws-Compact Mappings in Banach Spaces

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.

Browder-Krasnoselskii-Type Fixed Point Theorems in Banach Spaces

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.

Fixed point theory on extension-type spaces and essential maps on topological spaces

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

Existence results of Brezis-Browder type for systems of Fredholm integral equations

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...

Existence results of Brezis-Browder type for systems of Fredholm integral equations

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...

An Approximation Approach to Eigenvalue Intervals for Singular Boundary Value Problems with Sign Changing and Superlinear Nonlinearities

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.

Existence and multiplicity of solutions for some three-point nonlinear boundary value problems

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

Construction of upper and lower solutions for singular discrete initial and boundary value problems via inequality theory

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.

Multiplicity Results via Topological Degree for Impulsive Boundary Value Problems under Non-Well-Ordered Upper and Lower Solution Conditions

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.

Dead Core Problems for Singular Equations with -Laplacian

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 .

A Dual of the Compression-Expansion Fixed Point Theorems

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

Constant Sign and Nodal Solutions for Problems with the -Laplacian and a Nonsmooth Potential Using Variational Techniques

We consider a nonlinear elliptic equation driven by the -Laplacian with a nonsmooth potential (hemivariational inequality) and Dirichlet boundary condition. Using a variational approach based on nonsmooth critical point theory together with the method of upper and lower solutions, we prove the existence of at least three nontrivial smooth solutions: one positive, the second...

A Leray-Schauder alternative for weakly-strongly sequentially continuous weakly compact maps

Waterloo , ON , Canada N2L 3G1 E-mail address: 1 Donal O'Regan: Department of Mathematics, National University of Ireland , Galway , Ireland E-mail address: 2 Ravi P. Agarwal: Department of Mathematical

On the oscillation of certain third-order difference equations

Hindawi Publishing Corporation Advances in Difference Equations RAVI P. AGARWAL SAID R. GRACE DONAL O'REGAN We establish some new criteria for the oscillation of third-order difference equations