The p-Laplacian evolution equation in metric measure spaces has been studied as the gradient flow L2 of p-Cheeger energy (for 1<p<∞). In this paper, using first-order differential structure on a space introduced by Gigli, we characterise subdifferential energy. This gives rise to new definition operator spaces, which allows us work with more detail. way, introduce notion solutions spaces. For p...

Here, we find the characteristics polynomial of normalized Laplacian of a tree. The coefficients of this polynomial are expressed by the higher order general Randić indices for matching, whose values depend on the structure of the tree. We also find the expression of these indices for starlike tree and a double-starlike tree, Hm(p, q). Moreover, we show that two cospectral Hm(p, q) of the same ...

We prove a strong maximum principle for semicontinuous viscosity subsolutions or supersolutions of fully nonlinear degenerate elliptic PDE's, which complements the results of 17]. Our assumptions and conclusions are diierent from those in 17], in particular our maximum principle implies the nonexistence of a dead core. We test the assumptions on several examples involving the p-Laplacian and th...

This paper is concerned with the integral type boundary value problems of the second order differential equations with one-dimensional p-Laplacian  [ρ(t)Φ(x′(t))]′ + f(t, x(t), x′(t)) = 0, t ∈ (0, 1), φ1(x(0)) = ∫ 1 0 g(s)φ1(x(s))ds, φ2(x ′(1)) = ∫ 1 0 h(s)φ2(x ′(s))ds. Sufficient conditions to guarantee the existence of at least three positive solutions of this BVP are established. An exampl...

In this paper, we firstly obtain the existence of the monotone positive solutions and establish a corresponding iterative scheme for the following mixed-order four-point boundary value problem with p-Laplacian (φp(D α 0+u(t))) ′ + a(t)f(t, u(t), u′(t)) = 0, 0 < t < 1, u′(0)− βu(ξ) = 0, u′′(0) = 0, u′(1) + γu(η) = 0. Unlike many other fractional boundary value problem with p-Laplacian, the nonli...