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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We provide fundamental properties of the first eigenpair for fractional$p$-Laplacian eigenvalue problems under singular weights, which is related toHardy type inequality, and also show that the second eigenvalue iswell-defined. We obtain a-priori bounds and the continuity of solutions toproblems with such singular weights with some additional assumptions. Moreover,applying the above results, we show a global bifurcation emenating from thefirst eigenvalue, the Fredholm alternative for non-resonant problems, andobtain the existence of infinitely many solutions for some nonlinear problemsinvolving singular weights. These are new results, even for (fractional)Laplacian.

Properties of eigenvalues and some regularities on fractional $p$-Laplacian with singular weights