$p$-Laplacian and Lienard-Type Equation

Asymptotic Behavior of Solution for p-Laplacian Type Wave Equation

MULTIVALUED p-LIENARD SYSTEMS

In the last decade, there have been many papers dealing with second-order multivalued boundary value problems. We mention the works of Erbe and Krawcewicz [5, 6], Frigon [7, 8], Halidias and Papageorgiou [9], Kandilakis and Papageorgiou [11], Kyritsi et al. [12], Palmucci and Papalini [17], and Pruszko [19]. In all the above works, with the exception of Kyritsi et al. [12], p = 2 (linear differ...

The Kirchhoff Equation for the P – Laplacian

wt t (t, x)− K (‖wx (t, ·)‖ β Lr (R))a(wx (t, x))wxx (t, x) = 0, (2) w(0, x) = 8(x), wt (0, x) = 9(x), where K is an arbitrary function, sufficiently smooth and taking only positive values; and a = a(s) behaves like |s|p−2 near s = 0. The detailed assumptions on K , r , β, and a are given in (3), (4) and Condition 1 below. For K = K (s) = c1 + c2s (c1, c2 > 0) and p = r = β = 2, we get the famo...

On a nonlinear Hadamard type fractional differential equation with p-Laplacian operator and strip condition

Under certain nonlinear growth conditions of the nonlinearity, we investigate the existence of solutions for a nonlinear Hadamard type fractional differential equation with strip condition and p-Laplacian operator. At the end, two examples are given to illustrate our main results. ©2016 All rights reserved.

Existence and multiplicity of solutions for a Neumann-type p(x)-Laplacian equation with nonsmooth potential

In this paper we study Neumann-type p(x)-Laplacian equation with nonsmooth potential. Firstly, applying a version of the non-smooth three-critical-points theorem we obtain the existence of three solutions of the problem in W (Ω). Finally, we obtain the existence of at least two nontrivial solutions, when α− > p.