关键词: 拓扑度, 不动点, 非平凡解和正解, Euler-Bernoulli梁方程

Abstract: Under some conditions about corresponding principal eigenvalue of  linear operator, we prove the existence of nontrivial solutions and positive solutions of boundary value problem for the semipositive nonlinear Euler-Bernoulli beam equations with simply supported beam boundary condition by using the topological degree method and the fixed point theory.

Key words: topological degree, fixed point, nontrivial solution and positive solution, Euler-Bernoulli beam equations