EXISTENCE OF MULTIPLE POSITIVE RADIAL SOLUTIONS TO ELLIPTIC EQUATIONS IN AN ANNULUS

Abstract

In this paper, we use Leggett-Williams multiple fixed point theorems to obtain sufficient conditions for the existence of at least one or two positive radial solutions of the equation −∆u = λg(|x|)f(u), R1 < |x| < R2, x ∈ RN , N ≥ 2 subject to a linear mixed boundary condition at R1 and R2. AMS Subject Classification: 35J08, 35J25, 35J57, 34K13, 34C10, 34C27