Asymptotic estimates for PDE with p-Laplacian and damping

Inverse nodal problem for p-Laplacian with two potential functions

In this study, inverse nodal problem is solved for the p-Laplacian operator with two potential functions. We present some asymptotic formulas which have been proved in [17,18] for the eigenvalues, nodal points and nodal lengths, provided that a potential function is unknown. Then, using the nodal points we reconstruct the potential function and its derivatives. We also introduce a solution of i...

Asymptotic Behavior of Solution for p-Laplacian Type Wave Equation

CALDERÓN-ZYGMUND ESTIMATES FOR PARABOLIC p(x, t)-LAPLACIAN SYSTEMS

We prove local Calderón-Zygmund estimates for weak solutions of the evolutionary p(x, t)-Laplacian system ∂tu− div ( a(x, t)|Du|p(x,t)−2Du ) = div ( |F |p(x,t)−2F ) under the classical hypothesis of logarithmic continuity for the variable exponent p(x, t). More precisely, we show that the spatial gradient Du of the solution is as integrable as the right-hand side F , i.e. |F |p(·) ∈ Lqloc =⇒ |D...

Oscillation criteria for p-Laplacian delay dynamic equations with damping on time scales

on a time scale T, here (s) = |s|γ –2s, γ > 1 with a, p and q are positive real-valued rd-continuous functions defined on T. By using the Riccati transformation technique and integral averaging technique, some new sufficient conditions, which ensure that every solution oscillates, are established. Our results in this paper not only extend and improve the known results, but also unify the result...

Boundary Asymptotic and Uniqueness of Solution for a Problem with p(x)-Laplacian