Construction of variational factors for quasilinear second order partial differential equations

Abstract

Using our methodology the next results are delivered. For concrete types of quasi-linear partial differential equations (PDE) for which classical variational principle is fulfilled, are constructed in explicit form some variational factors. It has also been demonstrated the existence of some particular cases where the above mentioned solution does not exist. For certain linear PDE types such solutions are described. Concerning linear PDE hyperbolic and elliptic types, the solutions led to lower bounded functionals.