EXISTENCE OF POSITIVE SOLUTIONS FOR SOME NONLINEAR ELLIPTIC PROBLEMS IN UNBOUNDED DOMAINS OF Rn.

This paper deals with a class of nonlinear elliptic equations in an unbounded domain D of ℝⁿ, n ≥ 3, with a nonempty compact boundary, where the nonlinear term satisfies some appropriate conditions related to a certain Kato class K^∞(D). Our purpose is to give some existence results and asymptotic behaviour for positive solutions by using the Green function approach and the Schauder fixed point theorem. [ABSTRACT FROM AUTHOR]