The aim of the present paper is to investigate some properties periodic solutions a nonlinear autonomous parabolic systems with condition. We differential equations using an integral manifolds method theory oscillations. prove existence in system weak diffusion on circle. study and stability arbitrarily large finite number cycles for diffusion. solution equation sought form traveling wave. A re...

We establish the intrinsic Harnack inequality for nonnegative solutions of the parabolic p-Laplacian equation by a proof that uses neither the comparison principle nor explicit self-similar solutions. The significance is that the proof applies to quasilinear p-Laplacian-type equations, thereby solving a long-standing problem in the theory of degenerate parabolic equations. 1. Main results Let E...

In this paper, we consider the quasilinear elliptic equation in a smooth bounded domain. By using the method of lower and upper solutions, we study the existence, asymptotic behavior near the boundary and uniqueness of the positive blow-up solutions for quasilinear elliptic equation with nonlinear gradient term.