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(u0))0 = 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].
RICH DYNAMICS IN PLANAR SYSTEMS WITH HETEROGENEOUS NONNEGATIVE WEIGHTS
Zanolin F.
2023-01-01
Abstract
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(u0))0 = 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].File in questo prodotto:
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