Existence of image solutions and/or positive solutions to a semipositone elastic beam equation Original Research Article

The existence of nn solutions and/or positive solutions is established for a nonlinear fourth-order two-point boundary value problem where nn is an arbitrary natural number and the nonlinear term has a nonpositive lower bound. In mechanics, the problem describes deformation of the elastic beam whose two ends are simply supported. The main results show that the problem has at least nn solutions and/or positive solutions provided that the “heights” of the nonlinear term are appropriate on some bounded sets.