【摘要】 考虑有界区域Ω RN上非齐次半线性椭圆型方程-Δu=up+λf(x)在齐次混合边值条件(即第三边值问题) u=0下的正解的存在性和不存在性,其中p∈(1,N+2 n+αuN-2),N>2,或p∈(1,∞),1≤N Ω≤2,f(x)∈L∞(Ω),证明了存在2个常数λ ≥λ >0,使当λ∈(0,λ )时,上述问题至少存在2个正解,而当λ>λ 时没有正解.更多还原

【Abstract】 We consider the existence and nonexistence of positive solutions for the following nonhomogeneous semilinear elliptic problem -Δu=up+λf(x),x∈Ω,un+αu=0,x∈Ω,where ΩRN is a bounded domain,p∈(1,N+2N-2),N>2,p∈(1,∞),1≤N≤2,f(x)∈L∞(Ω).We prove that there exists two positive numbers λ≥λ>0 such that the problem has at least two positive solutions for λ∈(0,λ) while has no positive solution for λ>λ.更多还原