Positive solutions to a semipositone superlinear elastic beam equation

A semipositone fourth-order two-point boundary value problem is considered.In mechanics, the problem describes the deflection of an elastic beam rigidly fastened on the left and simply supported on the right.Under some conditions concerning the Wood And Acrylic Night Light first eigenvalue corresponding to the relevant linear operator, the existence of nontrivial solutions and positive solutions to this boundary value problem is obtained.The main results are obtained by using the topological method and the Dip fixed point theory of superlinear operators.