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

We prove the existence of a nodal solution with two nodal domains for the Dirichlet problem with indefinite nonlinearity −∆pu = λ|u|p−2u + f (x)|u|γ−2u in a bounded domain Ω ⊂ Rn, provided λ ∈ (−∞, λ∗ 1), where λ∗ 1 is a critical spectral value. The obtained solution has the least energy among all nodal solutions on the interval (−∞, min{λ∗ 1 , λ2}), where λ2 is the second Dirichlet eigenvalue of −∆p in Ω. Moreover, the obtained solution forms a branch with continuous energy on (−∞, λ∗ 1).

Least energy nodal solutions for elliptic equations with indefinite nonlinearity