In this article we obtain global positive and radially symmetric solutions to the system of nonlinear elliptic equations $$ \operatorname{div}\big(\phi_j(|\nabla u|) \nabla u\big) +a_j(x)\phi_j(|\nabla |\nabla u| =p_j(x)f_j(u_1(x),\dots,u_k(x))\,, in particular Laplace's equation \Delta u_j(x) where \(j=1,\dots,k\), \( x\in\mathbb{R}^N\), \(N\geq 3\), \(\Delta \) is Laplacian operator, \(\nabla...

In the present work, chemotaxis-Naiver-Stokes system with rapidly decaying diffusivities \begin{document}$ \begin{eqnarray*} { \bf{(KSNS)} }\ \ \left\{ \begin{array}{llll} n_{t}+u\cdot\nabla n = \nabla\cdot(D(n)\nabla n)-\nabla\cdot(S(n)\nabla c), &&x\in\Omega, \, t>0, \\ c_{t}+u\cdot\nabla c \Delta - c+ n, u_{t}+\kappa(u\cdot\nabla)u u +\nabla P+ n\nabla\Phi, \nabla\cdot 0, t>0\ ...

Differences are introduced as outputs of linear systems called differencers, being considered two classes: shift and scale-invariant. Several types presented, namely: nabla delta, bilateral, tempered, bilinear, stretching, shrinking. Both continuous discrete-time differences described. ARMA-type based on differencers exemplified. In passing, the incorrectness usual delta difference is shown.

We prove the existence of at least one positive solution to the time-scale, delta-nabla dynamic equation, (g(u∆))∇ + c(t)f(u) = 0, with boundary conditions, u(a) − B0(u(ν)) = 0 and u(b) = 0. Here, g(z) = |z|p−2z for p > 1, ν ∈ (a, b), f and c are left-dense continuous, and B0 is a function “bounded” by two linear rays.

The paper discusses fractional integrals and derivatives appearing in the so-called (q, h)-calculus which is reduced for h = 0 to quantum calculus q 1 difference calculus. We introduce delta as well nabla version of these notions present their basic properties. Furthermore, we give comparisons with known results discuss possible extensions more general settings.