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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper we study the existence of sign-changing solutions for nonlinear problems involving the fractional Laplacian $$ left { textstylebegin{array}{l@{quad}l} (-Delta)^{s}u-lambda u=f(x,u),u0026xinOmega,  u=0,u0026xinmathbb{R}^{n}setminusOmega, end{array}displaystyle right . $$(0.1)where (Omegasubsetmathbb{R}^{n}) ((ngeq2)) is a bounded smooth domain, (sin(0,1)), ((-Delta)^{s}) denotes the fractional Laplacian, λ is a real parameter, the nonlinear term f satisfies superlinear and subcritical growth conditions at zero and at infinity. When (lambdaleq0), we prove the existence of a positive solution, a negative solution and a sign-changing solution by combing minimax method with invariant sets of descending flow. When (lambdageq lambda_{1}^{s}) (where (lambda_{1}^{s}) denotes the first eigenvalue of the operator ((-Delta)^{s}) in Ω with homogeneous Dirichlet boundary data), we prove the existence of a sign-changing solution by using a variation of linking type theorems.

Mountain pass and linking type sign-changing solutions for nonlinear problems involving the fractional Laplacian