López Gómez, JuliánMuñoz Hernández, EduardoZanolin, Fabio2024-01-162024-01-162023Julián López-Gómez, Eduardo Muñoz-Hernández, Fabio Zanolin. Rich dynamics in planar systems with heterogeneous nonnegative weights. Communications on Pure and Applied Analysis, 2023, 22(4): 1043-1098. doi: 10.3934/cpaa.2023020 shu1534-039210.3934/cpaa.2023020https://hdl.handle.net/20.500.14352/93485This paper studies the global structure of the set of nodal solutions of a generalized Sturm–Liouville boundary value problem associated to the quasilinear equation −(φ(u'))' = λu + a(t)g(u), λ ∈ R, where a(t) is non-negative with some positive humps separated away by intervals of degeneracy where a ≡ 0. When φ(s) = s this equation includes a generalized prototype of a classical model going back to Moore and Nehari [35], 1959. This is the first paper where the general case when λ ∈ R has been addressed when a ≥ 0. The semilinear case with a ≤ 0 has been recently treated by López-Gómez and Rabinowitz [28, 29, 30].engjournal article1553-5258https://doi.org/10.3934/cpaa.2023020restricted accessNonlinear differential equationsPlanar systemsDegenerate weightsMoore–Nehari equationNodal solutionsGlobal bifurcation theoryA priori boundsPoincaré mapsEcuaciones diferenciales1202.19 Ecuaciones Diferenciales Ordinarias1202.20 Ecuaciones Diferenciales en derivadas Parciales