The three-dimensional digital waveguide mesh is a method for modeling the propagation of sound waves in space. It provides a simulation of the state of the whole soundfield at discrete timesteps. The updating functions of the mesh can be formulated either using physical values of sound pressure or particle velocity, also called the Kirchhoff values, or using a wave decomposition of these instea...

a class of kirchhoff type systems with nonlinear boundary conditions considered in this paper. by using the method of nehari manifold, it is proved that the system possesses two nontrivial nonnegative solutions if the parameters are small enough.