Abstract
In Ben Mabrouk and Ben Mohamed (2006) [A. Ben Mabrouk, M.L. Ben Mohamed, On some critical and slightly super-critical sub-superlinear equations. Far East J. Appl. Math. 23(1) (2006) 73–90, Special Volume of PDEs; A. Ben Mabrouk, M.L. Ben Mohamed, Nodal solutions for some nonlinear elliptic equations, Appl. Math. Comp., in press,
doi:10.1016/j.amc.2006.08.003], it has proved some theoretical results dealing with some boundary value problem Δ
u
+
f(
u)
=
0 in
B and
u
=
0 on ∂
B, where
B is a domain in
R
d
with smooth boundary. In the present paper, we perform a difference scheme method to approximate the solution of a nonlinear evolutionary problem associated to the elliptic problem studied in Ben Mabrouk and Ben Mohamed (2006). We give at the end some numerical implementations based on a mixed sublinear superlinear term of the form
f(
u)
=
∣
u∣
p−1
u
+
λ∣
u∣
q−1
u.