arXiv subjects

Laura María Fernández-Pardo

Publications and source records attributed to Laura María Fernández-Pardo.

2 recordsLinked to original sources

arXiv2026

Multiple non-collision periodic solutions for second order singular differential systems with parameters

In this paper, new existence and multiplicity results for positive periodic solutions of singular second-order problems under sublinear and superlinear growth assumptions at infinity are established. Two aspects of our results should be highlighted in comparison with the existing literature. On the one hand, they allow for the consideration of systems exhibiting mixed behavior: sublinear in one component and superlinear in another. On the other hand, in the superlinear case, the existence of up to four positive solutions is established, whereas only two were obtained in previous works. Our approach is based on a recently established vectorial version of the Krasnoselskii-Guo fixed point theorem in product spaces.

math.CA↗

arXiv2026

Hybrid and Component-wise Leggett-Williams type Fixed Point Theorems in Product Spaces with Applications

In this paper, we present new multiplicity fixed point theorems for operators acting on Cartesian products of two normed linear spaces. We show that Leggett-Williams type conditions in each component of the system guarantee the existence of nine distinct fixed points, of which four of them are coexistence fixed points, i.e., points with all components nontrivial. In addition, a hybrid approach combining Leggett-Williams conditions in one component with Krasnosel'skii compression-expansion conditions in the other allows us to obtain three fixed points. As an application, we establish the existence of multiple positive solutions for nonlinear systems of second-order equations with two-point boundary conditions.

math.FA↗