The mean value theorem and converse theorem of one class the fourth-order partial differential equations

For the formal presentation about the definite problems of ultra-hyperbolic equations, the famous Asgeirsson mean value theorem has answered that Cauc hy problems are ill-posed to ultra-hyperbolic partial differential equation s of the second-order. So it is important to develop Asgeirsson mean value theorem. The mean value of solution for the higher order equation hay been discussed primarily and has no exact result at present. The mean value theo rem for the higher order equation can be deduced and satisfied generalized biaxial symmetry potential equation by using the result of Asgeirsson mean value theorem and the properties of derivation and integration. Moreover, t he mean value formula can be obtained by using the regular solutions of pot ential equation and the special properties of Jacobi polynomials. Its conve rse theorem is also proved. The obtained results make it possible to discus s on continuation of the solutions and well posed problem.