Periodic solutions of p-Laplacian systems with a nonlinear convection term

Periodic Solutions of p-Laplacian Systems with a Nonlinear Convection Term

((u1(x, t+ ω), (u2(x, t+ ω)) = (u1(x, t), u2(x, t)) in Q, where △pu = div(|∇u| p−2 ∇u) is the so-called p−Laplacian operator, Ω is a bounded convex subset in R , Q := Ω × (0, ω), S := ∂Ω × (0, ω), ∂Ω is the boundary of Ω and ω > 0. Precise conditions on ai, fi and hi will be given later. The system of form (S) is a class of degenerate parabolic systems and appears in the theory of non-Newtonian...

Research Article Periodic Solutions of Evolution m-Laplacian Equations witha Nonlinear Convection Term

where Ω RN (N 1) is a bounded domain with smooth boundary ∂Ω, ω > 0, m > 1, and b(u) is a nonlinear vector field such that b(u) k u β, with some k > 0, 0 β m 1. f (t) and h(x, t) are ω-periodic (in t) functions. Equation (1.1) is a class of degenerate parabolic equations and appears to be relevant in the theory of non-Newtonian fluids perturbed by nonlinear terms and forced by rather irregular ...

Existence of Periodic Solutions of p(t)-Laplacian Systems

In this paper, by using the least action principle in critical point theory, we obtain some existence theorems of periodic solutions for p(t)-Laplacian system  d dt (|u̇(t)|p(t)−2u̇(t)) = ∇F (t, u(t)) a.e. t ∈ [0, T ] u(0)− u(T ) = u̇(0)− u̇(T ) = 0, which generalize some existence theorems. 2010 Mathematics Subject Classification: 34C25, 35A15

EXISTENCE OF PERIODIC SOLUTIONS OF 2α-ORDER NONLINEAR FUNCTIONAL DIFFERENCE EQUATIONS WITH p−LAPLACIAN

The existence of periodic solutions of a higher order nonlinear functional difference equation with p-Laplacian is studied. Sufficient conditions for the existence of periodic solutions of such equation are established. The result is based on Mawhin′s continuation theorem. The methods used to estimate the priori bound on periodic solutions are very technical.

Existence of Periodic Solutions for a Class of Asymptotically p-Linear Discrete Systems Involving p-Laplacian