Corpus ID: 202537345

Nonnegative solutions for the fractional Laplacian involving a nonlinearity with zeros

@article{Alarcn2019NonnegativeSF,
  title={Nonnegative solutions for the fractional Laplacian involving a nonlinearity with zeros},
  author={S. Alarc{\'o}n and L. Iturriaga and Antonella Ritorto},
  journal={arXiv: Analysis of PDEs},
  year={2019}
}

S. Alarcón, L. Iturriaga, Antonella Ritorto

Published 2019

Mathematics

arXiv: Analysis of PDEs

We study the nonlocal nonlinear problem \begin{equation}\label{ppp} \left\{ \begin{array}[c]{lll} (-\Delta)^s u = \lambda f(u) & \mbox{in }\Omega, \\ u=0&\mbox{on } \mathbb{R}^N\setminus\Omega, \end{array} \right. \tag{$P_{\lambda}$} \end{equation} where $\Omega$ is a bounded smooth domain in $\mathbb{R}^N$\!,\,$N>2s$,\,$0<s<1$; $f:\mathbb{R}\rightarrow [0,\infty)$ is a nonlinear continuous function such that $f(0)=f(1)=0$ and $f(t)\sim |t|^{p-1}t$ as $t\rightarrow 0^+$, with $2<p+1<2^*_s$; and… CONTINUE READING

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