In this article, we first obtain an embedding result for the Sobolev spaces with variable-order, and then consider following Schrödinger–Kirchhoff type equations a+b∫Ω×Ω|ξ(x)−ξ(y)|p|x−y|N+ps(x,y)dxdyp−1(−Δ)ps(·)ξ+λV(x)|ξ|p−2ξ=f(x,ξ),x∈Ω,ξ=0,x∈∂Ω, where Ω is a bounded Lipschitz domain in RN, 1<p<+∞, a,b>0 are constants, s(·):RN×RN→(0,1) continuous symmetric function N>s(x,y)p all (x,...

Abstract In this paper, we study the oscillation of solutions for an even-order differential equation with middle term, driven by a p -Laplace operator form $$ \textstyle\begin{cases} ( r x ) \Phi _{p}[z^{ \kappa -1 } ] ^{\prime }+a _{p}[f z^{ ]+ \sum_{i=1}^{j}q_{i} _{p}[h z \delta _{i} ]=0, \\ \quad j\geq 1, &gt;0, r^{\prime +a \geq 0, x\geq x_{0}&gt;0. \end{cases}$$ <mml:math xmlns:mml="http:...