English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this article, we study the Fu\v{c}ik spectrum of the $p$-fractionalLaplace operator with nonlocal normal derivative conditions which is defined asthe set of all $(a,b)\in \mb R^2$ such that $$ \mc (F_p)\left\{\begin{array}{lr} \Lambda_{n,p}(1-\al)(-\Delta)_{p}^{\al} u + |u|^{p-2}u =\frac{\chi_{\Omega_\e}}{\e} (a (u^{+})^{p-1} - b (u^{-})^{p-1}) \;\quad\text{in}\; \Omega,\quad \\ \mc{N}_{\al,p} u = 0 \; \quad \mbox{in}\; \mb R^n\setminus \overline{\Omega}, \end{array} \right. $$ has a non-trivial solution$u$, where $\Omega$ is a bounded domain in $\mb R^n$ with Lipschitz boundary,$p \geq 2$, $n>p \al $, $\e, \al \in(0,1)$ and $\Omega{_\e}:=\{x \in \Omega:d(x,\pa \Omega)\leq \e \}$. We showed existence of the first non-trivial curve$\mc C$ of this spectrum which is used to obtain the variationalcharacterization of a second eigenvalue of the problem $\mc (F_p)$. We alsodiscuss some properties of this curve $\mc C$, e.g. Lipschitz continuous,strictly decreasing and asymptotic behaviour and nonresonance with respect tothe Fu\v{c}ik spectrum.

On the first curve of Fu\v{c}ik Spectrum Of $p$-fractional Laplacian Operator with nonlocal normal boundary conditions