Travelling wave solutions of the beam equation with jumping nonlinearity (Q6112509)

The authors study the existence of traveling wave solutions for the beam equation with jumping nonlinear terms: \[ u_{tt} + u_{xxxx} + \alpha u^{+} - \beta u^{-} + g(u) =1, \] where \(u^{\pm} = \max\{ \pm u, 0 \}\). The variational formulation and the mountain pass theorem play key role in the proof. Numerical results are also presented, and readers can see the possible profiles for the solutions.