López Gómez, JuliánMuñoz Hernández, EduardoZanolin, Fabio2025-08-252025-08-252025-07-09López-Gómez J, Muñoz-Hernández E, Zanolin F. Global multiplicity results in a Moore–Nehari type problem with a spectral parameter. J Diff Eqs. 2025 Dec 447; 5 December 2025, 11362810.1016/j.jde.2025.113628https://hdl.handle.net/20.500.14352/123341This paper analyzes the structure of the set of positive solutions of \eqref{1.1}, where $a\equiv a_h$ is the piece-wise constant function defined in \eqref{1.3} for some $h\in (0,1)$. In our analysis, $\l$ is regarded as a bifurcation parameter, whereas $h$ is viewed as a deformation parameter between the autonomous case when $a=1$ and the linear case when $a=0$. In this paper, besides establishing some of the multiplicity results suggested by the numerical experiments of \cite{CLGT-2024}, we have analyzed the asymptotic behavior of the positive solutions of \eqref{1.1} as $h\uparrow 1$, when the shadow system of \eqref{1.1} is the linear equation $-u''=\pi^2 u$. This is the first paper where such a problem has been addressed. Numerics is of no help in analyzing this singular perturbation problem because the positive solutions blow-up point-wise in $(0,1)$ as $h\uparrow 1$ if $\l<\pi^2$.engAttribution-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nd/4.0/journal articlehttps://doi.org/10.1016/j.jde.2025.113628https://www.sciencedirect.com/journal/journal-of-differential-equations/vol/447/suppl/Copen access517.9Moore-Nehari equationMultiplicity of positive solutionsPoint-wise blow-up to a metasolutionSpectral parameterEcuaciones diferenciales1202.19 Ecuaciones Diferenciales Ordinarias