Browsing Publications by Author "O'Regan, Donal"
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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 (20091026)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 setvalued maps in hyperconvex metric spaces
AminiHarandi, Alireza; Farajzadeh, Ali P.; O'Regan, Donal; Agarwal, Ravi P. (20081105)A best proximity pair for a setvalued 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 setvalued maps with respect to a homeomorphism ... 
Best proximity pairs theorems for continuous setvalued maps
AminiHarandi, Alireza; Farajzadeh, Ali P.; O'Regan, Donal; Agarwal, Ravi P. (20081230)A best proximity pair for a setvalued map F : A ○ B with respect to a setvalued map G : A ○ A is defined, and a new existence theorem of best proximity pairs for continuous setvalued maps is proved in nonexpansive ... 
BirkhoffKellogg theorems on invariant directions for multimaps
Agarwal, Ravi P.; O'Regan, Donal (20011211)We establish BirkhoffKellogg 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. 
Browderkrasnoselskiitype fixed point theorems in Banach spaces
Agarwal, Ravi P.; O'Regan, Donal; Taoudi, MohamedAziz (20100402)We present some fixed point theorems for the sum A+B of a weaklystrongly 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 setvalued maps in hyperconvex metric spaces
AminiHarandi, Alireza; Farajzadeh, Ali P.; Agarwal, Ravi P.; O'Regan, Donal (20081221)In hyperconvex metric spaces, we first present a coincidence point theorem for condensing setvalued selfmaps. Then we consider the best approximation problem and the best proximity problem for setvalued mappings that ... 
Constant sign and nodal solutions for problems with the pLaplacian and a nonsmooth potential using variational techniques
Agarwal, Ravi P.; Filippakis, Michael E.; O'Regan, Donal; Papageorgiou, Nikolaos S. (20090123)We consider a nonlinear elliptic equation driven by the pLaplacian with a nonsmooth potential (hemivariational inequality) and Dirichlet boundary condition. Using a variational approach based on nonsmooth critical point ... 
Constantsign solutions of a system of integral equations with integrable singularities
Agarwal, Ravi P.; O'Regan, Donal; Wong, P.J. (20070622)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 ... 
Constantsign solutions of a system of Volterra integral equations in Orlicz spaces
Agarwal, Ravi P.; O'Regan, Donal; Wong, P.J.Y. (20080922)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 φLaplacian
Agarwal, Ravi P.; O'Regan, Donal; Staněk, Svatoslav (200808)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 (20110223)The boundary value problems for degenerate anisotropic differential operator equations with variable coefficients are studied. Several conditions for the separability and Fredholmness in Banachvalued 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 φlaplacian 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 ψLaplacian. 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. (200704)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 convexpower condensing operators relative to the weak topology and applications to volterra integral equations
Agarwal, Ravi P.; O'Regan, Donal; Taoudi, MohamedAziz (20120622)In this paper we present new fixed point theorems for weakly sequentially continuous mappings which are convexpower condensing relative to a measure of weak noncompactness. Our fixed point results extend and improve several ... 
Fixed point theorems for wscompact mappings in Banach spaces
Agarwal, Ravi P.; O'Regan, Donal; Taoudi, MohamedAziz (20101124)We present new fixed point theorems for wscompact operators. Our fixed point results are obtained under Sadovskii, LeraySchauder, Rothe, Altman, Petryshyn, and FuriPera type conditions. An example is given to show the ... 
Fixed point theory for admissible type maps with applications
Agarwal, Ravi P.; O'Regan, Donal (20090720)We present new LeraySchauder 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 ... 
Fixed point theory for Mönchtype maps defined on closed subsets of Fréchet spaces: the projective limit approach
Agarwal, Ravi P.; O'Regan, Donal; Dshalalow, Jewgeni H. (2005)New LeraySchauder alternatives are presented for Mönchtype maps defined between Fréchet spaces. The proof relies on viewing a Fréchet space as the projective limit of a sequence of Banach spaces. 
A FuriPera theorem in Hausdorff topological spaces for acyclic maps
Agarwal, Ravi P.; O'Regan, Donal; Dshalalow, Jewgeni H. (2004)We present new FuriPera theorems for acyclic maps between topological spaces. 
General existence principles for nonlocal boundary value problems with ølaplacian and their applications
Agarwal, Ravi P.; O'Regan, Donal; Staněk, Svatoslav (20050512)The paper presents general existence principles which can be used for a large class of nonlocal boundary value problems of the form (ø(x′)) ′ = f1(t,x,x′) + f2(t,x,x′)F 1X + f3(t,x,x′)f2x,α(x) = 0, β(x) = 0, where fj satisfy ...