EXISTENCE OF THREE SOLUTIONS FOR THE DIRICHLET PROBLEM INVOLVING THE P-LAPLACIAN AND MINIMAX INEQUALITY FOR RELEVANT FUNCTIONALS

In this paper, two new Hamilton operators are defined and the algebra of dual split quaternions is developed using these operators. It is shown that finite screw motions in Minkowski 3-space can be expressed by dual-number ( 3×3 ) matrices in dual Lorentzian space. Moreover, by means of Hamilton operators, screw motion is obtained in 3-dimensional Minkowski space 3 R1 .