Abstract
We present some new oscillation criteria for second‐order neutral partial functional differential equations of the form , (x, t) ∈ Ω × R+ ≡ G, where Ω is a bounded domain in the Euclidean N‐space RN with a piecewise smooth boundary ∂Ω and Δ is the Laplacian in RN. Our results improve some known results and show that the oscillation of some second‐order linear ordinary differential equations implies the oscillation of relevant nonlinear neutral partial functional differential equations.
Highlights
Our results improve some known results and show that the oscillation of some second-order linear ordinary differential equations implies the oscillation of relevant nonlinear neutral partial functional differential equations
International Journal of Differential Equations or u x, t 0, x, t ∈ ∂Ω × R ≡ G, 1.3 where Δ is the Laplacian in Euclidean N-space RN, R : 0, ∞, Ω is a bounded domain in RN with a piecewise smooth boundary ∂Ω, ν denotes the unit exterior normal vector to ∂Ω, and g x, t is a nonnegative continuous function on ∂Ω × R
Our results show that the oscillation of some second-order linear ordinary differential equations implies the oscillation of relevant nonlinear second-order neutral partial functional differential 1.1, we can obtain some new oscillation theorems for 1.1, which do not need the condition of the integrals of the coefficient
Summary
Our results improve some known results and show that the oscillation of some second-order linear ordinary differential equations implies the oscillation of relevant nonlinear neutral partial functional differential equations
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