On Lyapunov-type inequalities for a certain class of partial differential equations. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Jleli, M.; Kirane, M.; Samet, B.
• Is Part Of: Applicable analysis. Volume 99:Issue 1(2020)
• Page Start: 40
• Page End: 49
• Publication Date: 2020-01-02
• Subjects: Lyapunov-type inequalities -- partial differential equations -- sign-changing criteria -- first eigenvalue; 35A23 -- 47F05 -- 34A12; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1484909
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: A Lyapunov-type inequality is established for the partial differential equation: − G γ u ( x, y ) = w ( x ) u ( x, y ), ( x, y ) ∈ Ω, u ( x, y ) = 0, ( x, y ) ∈ ∂Ω, where Ω = ] a, b [ × O, ( a, b ) ∈ R 2, a < b, O is an open bounded subset in R N, N ≥ 1, G γ is the differential operator given by G γ u ( x, y ) := ( ∂ 2 u / ∂ x 2 ) + x 2 γ Δ y u, γ ≥ 0, ( x, y ) ∈ Ω, and w ∈ C ( [ a, b ] ) . Next, some sign-changing criteria are obtained for the nontrivial solutions to the considered problem.