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) i s the p-Laplacian, p is-an-element-of (1, infinity), and OMEGA is a bo unded smooth domain in R(n). For h(x) = 0 and f(x, u) satisfying prope r asymptotic spectral conditions, existence of a unique positive solut ion is obtained by invoking the sub-supersolution technique and the sp ectral method. For h(x) not-equal 0, with assumptions on asymptotic be havior of f(x, u) as u --> +/- infinity, an existence result is also p roved.