Sub-super solutions for (p-q) Laplacian systems
1 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 Department of Mathematics, Faculty of Mathematical Sciences University of Mazandaran, Babolsar, Iran
Boundary Value Problems 2011, 2011:52 doi:10.1186/1687-2770-2011-52Published: 2 December 2011
In this work, we consider the system:
where Ω is a bounded region in RN with smooth boundary ∂Ω, Δp is the p-Laplacian operator defined by Δpu = div (|∇u|p-2∇u), p, q > 1 and g (x) is a C1 sign-changing the weight function, that maybe negative near the boundary. f, h, a, b are C1 non-decreasing functions satisfying a(0) ≥ 0, b(0) ≥ 0. Using the method of sub-super solutions, we prove the existence of weak solution.