TY - JOUR
T1 - On Lyapunov-type inequalities for a certain class of partial differential equations
AU - Jleli, M.
AU - Kirane, M.
AU - Samet, B.
N1 - Funding Information:
This work was supported by King Saud University. The first and third authors would like to extend their sincere appreciation to the Deanship of Scientific Research at King Saud University for its funding of this research through the Research Group Project No RGP-1436-034.
Publisher Copyright:
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2020/1/2
Y1 - 2020/1/2
N2 - A Lyapunov-type inequality is established for the partial differential equation: (Formula presented.) where Ω =]a, b[×O, (a, b) ∈ R2, aN, N ≥ 1, Gγ is the differential operator given by Gγ u(x, y) := (∂2u/∂x2) +x2γ∆yu, 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.
AB - A Lyapunov-type inequality is established for the partial differential equation: (Formula presented.) where Ω =]a, b[×O, (a, b) ∈ R2, aN, N ≥ 1, Gγ is the differential operator given by Gγ u(x, y) := (∂2u/∂x2) +x2γ∆yu, 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.
KW - first eigenvalue
KW - Lyapunov-type inequalities
KW - partial differential equations
KW - sign-changing criteria
UR - http://www.scopus.com/inward/record.url?scp=85048520006&partnerID=8YFLogxK
U2 - 10.1080/00036811.2018.1484909
DO - 10.1080/00036811.2018.1484909
M3 - Article
AN - SCOPUS:85048520006
SN - 0003-6811
VL - 99
SP - 40
EP - 49
JO - Applicable Analysis
JF - Applicable Analysis
IS - 1
ER -