An elliptic semilinear equation with source term and boundary measure data: The supercritical case

We give new criteria for the existence of weak solutions to an equation with a super linear source term -Delta u = u(q) in Omega, u = sigma on partial derivative Omega where Omega is either a bounded smooth domain or R-+(N), q > 1 and sigma is an element of m(+)(partial derivative Omega) is a nonnegative Radon measure on partial derivative Omega. One of the criteria we obtain is expressed in terms of some Bessel capacities on partial derivative Omega. We also give a sufficient condition for the existence of weak solutions to equation with source mixed terms. -Delta u = vertical bar u vertical bar(q1-1)u vertical bar del u vertical bar(q2) in Omega, u = sigma on partial derivative Omega where q(1), q(2) >= 0, q(1) + q(2) >1, q(2) < 2, sigma is an element of m(partial derivative Omega) is a Radon measure on partial derivative Omega. (C) 2015 Elsevier Inc. All rights reserved.