Abstract
In this article, we discuss the existence of positive solutions by using sub-super solutions concepts of the following p(x)-Kirchhoff system:
{-M(I(0()u))Delta(p(x))u = lambda(p(x)) [lambda(1)f(v) + mu(1)h(u)] in Omega, -M(I(0()u))Delta(p(x))u = lambda(p(x)) [lambda(2)f(v) + mu(2)h(u)] in Omega, u = nu = 0 on partial derivative Omega,
where Omega subset of R-N is a bounded smooth domain with C-2 boundary partial derivative Omega, Delta(p(x))u = div(vertical bar del u vertical bar(p(x)-2)del u), p(x) is an element of C-1 ((Omega) over bar), with 1 < p(x) , is a function satisfying 1 < p(-) = inf(Omega) p(x) <= p(+) = sup(Omega) p(x) < infinity, lambda,lambda(1),lambda(2), mu(1) and mu(2) are positive parameters , I-0 (u) = integral(Omega) 1/p(x) vertical bar del vertical bar p((x)) dx, and M(t) is a continuous function.