EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF THE P-LAPLACE EQUATIONS

We are concerned with the existence of solutions of -DELTA(p)u = f(x,u) + h(x) in OMEGA, u = 0 on partial derivative OMEGA, where DELTA(p) is the p-Laplacian, p is-an-element-of (1, infinity), and OMEGA is a bounded smooth domain in R(n). For h(x) = 0 and f(x, u) satisfying proper asymptotic spectral conditions, existence of a unique positive solution is obtained by invoking the sub-supersolution technique and the spectral method. For h(x) not-equal 0, with assumptions on asymptotic behavior of f(x, u) as u --> +/- infinity, an existence result is also proved.