Uniqueness of nodal radial solutions to nonlinear elliptic equations in the unit ball

Abstract

In this paper, we study the uniqueness of nodal radial solutions to nonlinear elliptic equations in the unit ball in . Under suitable conditions, we prove that, for any given positive integer , the problem we considered has at most one solution possessing exactly nodes. Together with the results presented by Nagasaki [J. Fac. Sci. Univ. Tokyo Sect. IA Math. 36 (2): 211–232, 1989] and Tanaka [Proc. Roy. Soc. Edinburgh Sect. A. 138 (6): 1331–1343, 2008], we can prove that more types of nonlinear elliptic equations have the uniqueness of nodal radial solutions.