%0 Journal Article
%A López Gómez, Julián
%A Muñoz Hernández, Eduardo
%A Zanolin, Fabio
%T Rich dynamics in planar systems with heterogeneous nonnegative weights
%D 2023
%@ 1534-0392
%U https://hdl.handle.net/20.500.14352/93485
%X This 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].
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