2024/12/16 by Tapia, José Carmona, Antonio J. Martínez Aparicio, Aparicio, Antonio J. Martínez +2 · 2 citations
Computer Science · Mathematics · #35B32 #35B40 #35J25 #35J61 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2412.11690
openalex publication_date 2024/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the behavior of multiple continua of solutions to the semilinear elliptic problem \begincases -Δu = λf(u) amp; in Ω, u=0 amp; on ∂Ω, \endcases where Ω is a bounded open subset of \reN and f is a nonnegative continuous real function with multiple zeros. We analyze both the behavior of unbounded continua of solutions having norm between consecutive zeros of f, and the asymptotic behavior of the multiple unbounded continua in the case in which f has a countable infinite set of positive zeros. In both cases, we pay special attention to the multiplicity results they give rise to. For the model cases f(t) = tr(1+sin t) and f(t) = tr (1+sin (1)/(t)) with r≥ 0 we show the surprising fact that there are some values of r for which every λ>0 is a bifurcation point (either from infinity or from zero) that is not a branching point.