关键词: 2m阶椭圆方程, 正径向解, 拓扑度理论, 半正

Abstract: By using topological degree theory, the author studies the existence of positive radial solutions of 2m order semipositone elliptic equations in the annulus, where λ>0 is a parameter, m≥1 is a positive integer,  Ω={x∈Rⁿ; a<|x|<b}(n>2m), 0<a<b<∞, f∈C(［a,b］×［0,∞),R).  The results show that there exists λ₀>0, so that the above problem 
has at least one positive radial solution when λ₀ under suitable conditions.

Key words: 2m order elliptic equations, positive radial solution, topological degree theory, semipositone