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 existence/multiplicity results for thefollowing variable order nonlocal Choquard problem with variable exponents\begin{equation*} \begin{array}{rl}(-\Delta)_{p(\cdot)}^{s(\cdot)}u(x)&=\lambda|u(x)|^{\alpha(x)-2}u(x)+\left(\DD\int_\Omega\frac{F(y,u(y))}{|x-y|^{\mu(x,y)}}dy\right)f(x,u(x)),\\&~\hspace{6cm} x\in \Omega, \\ u(x)&=0 ,\hspace{20mm} x\in \Omega^c:=\mathbbR^N\setminus\Omega, \end{array} \end{equation*} where $\Om\subset\mathbb R^N$is a smooth and bounded domain, $N\geq 2$, $p,s,\mu$ and $\alpha$ arecontinuous functions on $\mathbb R^N\times\mathbb R^N$ and $f(x,t)$ iscontinuous function with $F(x,t):=\displaystyle\int_{0}^{t} f(x,s)ds$. Undersuitable assumption on $s,p,\mu,\alpha$ and $f(x,t)$, first we study theanalogous Hardy-Sobolev-Littlewood-type result for variable exponents suitablefor the fractional Sobolev space with variable order and variable exponents.Then we give the existence/multiplicity results for the above equation.

Multiplicity and uniform estimate for a class of variable order fractional $p(x)$-Laplacian problems with concave-convex nonlinearities