The Existence Of Nonnegative Solutions Of Inhomogeneous P-lapace Equation With Indefinited Data

Let Ω Rn be a smooth boundary domain, f(x) F = Ca(Ω)\{0}, 0 < a < 1. We consider Dirichlet problem of inhomogeneous p-Laplace equationWhere is so called p-Laplace operator.The main purpose of this paper is to identify necessary and sufficient conditions on Ω and f(x) which ensure the existence, or multiplicities of nonnegative solutions for the problem (*). The strategy to overcome corresponding difficulties is to construct the nonnegative subsolution of problem (1.1) and analyze the asymptotic behavior of the solution u\ of problem (1.1) as λ-0 or λ - . In fact, through those analyse, we found that the existence of nonnegative solution of problem (1.1) is closely related to the solvability of the following problem:also related to the following homogeneous problem:...