Uncountable sets of finite energy solutions for semilinear elliptic problems in exterior domains

Abstract

In this article we discuss conditions suitable for the existence of asymptotically vanishing positive solutions for the following semilinear elliptic problem △ u ( x ) + f ( x , u ( x ) ) + g ( x ) x ⋅ ∇ u ( x ) = 0 , where x ∈ R n and ‖ x ‖ > R . The main result of our investigation is the construction of uncountable sets of minimal solutions which have finite energy in a neighbourhood of infinity. We apply an iteration scheme based on the subsolution and supersolution method. Our approach allows us to consider sublinear as well as superlinear problems without radial symmetry.