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- W4288357440 abstract "We deal with the periodic boundary value problem associated with the parameter-dependent second-order nonlinear differential equation begin{equation*} u'' + cu' + bigr{(} lambda a^{+}(x) - mu a^{-}(x) bigr{)} g(u) = 0, end{equation*} where $lambda,mu>0$ are parameters, $cinmathbb{R}$, $a(x)$ is a locally integrable $P$-periodic sign-changing weight function, and $gcolonmathopen{[}0,1mathclose{]}tomathbb{R}$ is a continuous function such that $g(0)=g(1)=0$, $g(u)>0$ for all $uinmathopen{]}0,1mathclose{[}$, with superlinear growth at zero. A typical example for $g(u)$, that is of interest in population genetics, is the logistic-type nonlinearity $g(u)=u^{2}(1-u)$. Using a topological degree approach, we provide high multiplicity results by exploiting the nodal behaviour of $a(x)$. More precisely, when $m$ is the number of intervals of positivity of $a(x)$ in a $P$-periodicity interval, we prove the existence of $3^{m}-1$ non-constant positive $P$-periodic solutions, whenever the parameters $lambda$ and $mu$ are positive and large enough. Such a result extends to the case of subharmonic solutions. Moreover, by an approximation argument, we show the existence of a countable family of globally defined solutions with a complex behaviour, coded by (possibly non-periodic) bi-infinite sequences of $3$ symbols." @default.
- W4288357440 created "2022-07-29" @default.
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- W4288357440 date "2019-05-12" @default.
- W4288357440 modified "2023-10-16" @default.
- W4288357440 title "High multiplicity and chaos for an indefinite problem arising from genetic models" @default.
- W4288357440 doi "https://doi.org/10.48550/arxiv.1905.04671" @default.
- W4288357440 hasPublicationYear "2019" @default.
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