关键词: 存在性, 多解, 正解, 锥

Abstract: By using fixed point theorem of cone expansion-compression, the author studies the existence, nonexistence and multiplicity of positive solutions for the elastic beam problem with sliding supports at both ends, where ρ∈(0,π/2) is a constant, λ is a positive parameter, f∈C(［0,1］×［0,+∞),［0,+∞)).

Key words: existence, multiplicity, positive solution, cone