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Donal O’Regan

Abstract

This paper presents general topological coincidence principles for multivalued maps defined on subsets of completely regular topological spaces.

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Donal O’Regan

Abstract

We present a Leray–Schauder type alternative for a general class of maps. This enables us to obtain some Birkhoff–Kellogg type results and a Furi–Pera result.

Open access

Baoqiang Yan, Donal O’Regan and Ravi P. Agarwal

Abstract

In this paper we discuss the existence of a solution between wellordered subsolution and supersolution of the Kirchhoff equation. Using the sub-supersolution method together with a Rabinowitz-type global bifurcation theory, we establish the existence of positive solutions for Kirchhoff-type problems when the nonlinearity is singular or sign-changing. Moreover, we obtain some necessary and sufficient conditions for the existence of positive solutions for the problem when N = 1.

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Baoqiang Yan, Donal O’Regan and Ravi P. Agarwal

Abstract

In this paper using a fixed point theory on a cone we present some new results on the existence of multiple positive solutions for singular nonlocal boundary value problems involving integral conditions with derivative dependence.

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Gabriele Bonanno, Giuseppina D’Aguì and Donal O’Regan

Abstract

In this paper the existence of two positive solutions for a Dirichlet problem having a critical growth, and depending on a real parameter, is established. The approach is based on methods which are totally variational, unlike the fundamental result of Ambrosetti, Brezis and Cerami where a clever combination of topological and variational methods is used in order to obtain the same conclusion. In addition, a numerical estimate of real parameters, for which the two solutions are obtained, is provided. Our main tool is a local minimum theorem.