Liouville-type theorems for elliptic equations in half-space with mixed boundary value conditions

Abstract

In this paper we study the nonexistence of solutions, which are stable or stable outside a compact set, possibly unbounded and sign-changing, of some nonlinear elliptic equations with mixed boundary value conditions. The main methods used are the integral estimates and the monotonicity formula.

Keywords

• liouville theorem
• stable solutions
• nonlinear boundary value condition
• stability outside a compact set
• monotonicity formula
• 35j55
• 35j65
• 35b33
• 35b65.