Browsing College of Engineering and Science by Author "O'Regan, Donal"

An approximation approach to eigenvalue intervals for singular boundary value problems with sign changing and superlinear nonlinearities

Lü, Haishen; Agarwal, Ravi P.; O'Regan, Donal (2009-10-26)

This paper studies the eigenvalue interval for the singular boundary value problem u″ = g (t, u) + λ h (t, u), t ∈(0, 1),u (0) = 0 = u (1), where g + h may be singular at u = 0, t = 0, 1, and may change sign and be superlinear ...

Best proximity pairs for upper semicontinuous set-valued maps in hyperconvex metric spaces

Amini-Harandi, Alireza; Farajzadeh, Ali P.; O'Regan, Donal; Agarwal, Ravi P. (2008-11-05)

A best proximity pair for a set-valued map F : A → B with respect to a map g : A → A is defined, and new existence theorems of best proximity pairs for upper semicontinuous set-valued maps with respect to a homeomorphism ...

Best proximity pairs theorems for continuous set-valued maps

Amini-Harandi, Alireza; Farajzadeh, Ali P.; O'Regan, Donal; Agarwal, Ravi P. (2008-12-30)

A best proximity pair for a set-valued map F : A -○ B with respect to a set-valued map G : A -○ A is defined, and a new existence theorem of best proximity pairs for continuous set-valued maps is proved in nonexpansive ...

Birkhoff-Kellogg theorems on invariant directions for multimaps

Agarwal, Ravi P.; O'Regan, Donal (2001-12-11)

We establish Birkhoff-Kellogg type theorems on invariant directions for a general class of maps. Our results, in particular, apply to Kakutani, acyclic, O'Neill, approximable, admissible, and script U signCK maps.

Browder-krasnoselskii-type fixed point theorems in Banach spaces

Agarwal, Ravi P.; O'Regan, Donal; Taoudi, Mohamed-Aziz (2010-04-02)

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

Coincidence point, best approximation, and best proximity theorems for condensing set-valued maps in hyperconvex metric spaces

Amini-Harandi, Alireza; Farajzadeh, Ali P.; Agarwal, Ravi P.; O'Regan, Donal (2008-12-21)

In hyperconvex metric spaces, we first present a coincidence point theorem for condensing set-valued self-maps. Then we consider the best approximation problem and the best proximity problem for set-valued mappings that ...

Constant sign and nodal solutions for problems with the p-Laplacian and a nonsmooth potential using variational techniques

Agarwal, Ravi P.; Filippakis, Michael E.; O'Regan, Donal; Papageorgiou, Nikolaos S. (2009-01-23)

We consider a nonlinear elliptic equation driven by the p-Laplacian with a nonsmooth potential (hemivariational inequality) and Dirichlet boundary condition. Using a variational approach based on nonsmooth critical point ...

Constant-sign solutions of a system of integral equations with integrable singularities

Agarwal, Ravi P.; O'Regan, Donal; Wong, P.J. (2007-06-22)

We consider the following systems of Fredholm integral equations and the system of Volterra integral equations where the nonlinearities fi, 1 ≤ i ≤ n may be singular in the independent variable and may also be singular at ...

Constant-sign solutions of a system of Volterra integral equations in Orlicz spaces

Agarwal, Ravi P.; O'Regan, Donal; Wong, P.J.Y. (2008-09-22)

We consider the following system of Volterra intergral equations uu1(t) = gi(t, s)fi(s, u1(s), u2(s), · · ·, un(s))ds, a.e. t ∈ [0,T], 1 ≤ i ≤ n. Criteria are offered for the existence of one and more constantsign solutions ...

Dead cores of singular Dirichlet boundary value problems with φ-Laplacian

Agarwal, Ravi P.; O'Regan, Donal; Staněk, Svatoslav (2008-08)

The paper discusses the existence of positive solutions, dead core solutions and pseudodead core solutions of the singular Dirichlet problem (ϕ(u′))′ = λf(t, u, u′), u(0) = u(T) = A. Here λ is the positive parameter, A > ...

Degenerate anisotropic differential operators and applications

Shakhmurov, Veli B.; Agarwal, Ravi P.; O'Regan, Donal (2011-02-23)

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 Lp spaces are given. ...

Differential inclusions on proximate retracts of separable Hilbert spaces

Agarwal, Ravi P.; O'Regan, Donal (2006)

New existence results are presented which guarantee the existence of viable solutions to differential inclusions in separable Hilbert spaces. Our results rely on the existence of maximal solutions for an appropriate ...

An existence principle for nonlocal difference boundary value problems with φ-laplacian and its application to singular problems

Agarwal, Ravi P.; O'Regan, Donal; Staněk, Svatoslav (2008)

The paper presents an existence principle for solving a large class of nonlocal regular discrete boundary value problems with the ψ-Laplacian. Applications of the existence principle to singular discrete problems are given.

Existence to singular boundary value problems with sign changing nonlinearities using an approximation method approach

Lü, Haishen; O'Regan, Donal; Agarwal, Ravi P. (2007-04)

This paper studies the existence of solutions to the singular boundary value problem {−u′′=g(t,u)+(h,u),t∈(0,1),u(0)=0=u(1), {−u″=g(t,u)+(h,u),t∈(0,1),u(0)=0=u(1), , where g: (0, 1) × (0, ∞) → ℝ and h: (0, 1) × [0, ∞) ...

Fixed point theorems for convex-power condensing operators relative to the weak topology and applications to volterra integral equations

Agarwal, Ravi P.; O'Regan, Donal; Taoudi, Mohamed-Aziz (2012-06-22)

In this paper we present new fixed point theorems for weakly sequentially continuous mappings which are convex-power condensing relative to a measure of weak noncompactness. Our fixed point results extend and improve several ...