Some results about semilinear elliptic problems on half-spaces

Abstract

We prove some new results about the growth, the monotonicity and the symmetry of (possibly) unbounded non-negative solutions of −∆u = f (u) on half-spaces, where f is merely a locally Lipschitz continuous function. Our proofs are based on a comparison principle for solutions of semilinear problems on unbounded slab-type domains and on the moving planes method.

Keywords

• qualitative properties of solutions to semilinear elliptic equations
• moving planes method
• comparison principle