variational formulation for a generalized third order equation

A universal formulation is obtained for the construction of a variational principle for a general third-order differential equation, regardless of its self-adjoint condition. three illustrative examples are provided to demonstrate the convenience and efficacy of the proposed formulation.a universal formulation is obtained for the construction of a variational principle for a general third-order differential equation, regardless of its self-adjoint condition. three illustrative examples are provided to demonstrate the convenience and efficacy of the proposed formulation.a universal formulation is obtained for the construction of a variational principle for a general third-order differential equation, regardless of its self-adjoint condition. three illustrative examples are provided to demonstrate the convenience and efficacy of the proposed formulation.a universal formulation is obtained for the construction of a variational principle for a general third-order differential equation, regardless of its self-adjoint condition. three illustrative examples are provided to demonstrate the convenience and efficacy of the proposed formulation.a universal formulation is obtained for the construction of a variational principle for a general third-order differential equation, regardless of its self-adjoint condition. three illustrative examples are provided to demonstrate the convenience and efficacy of the proposed formulation.a universal formulation is obtained for the construction of a variational principle for a general third-order differential equation, regardless of its self-adjoint condition. three illustrative examples are provided to demonstrate the convenience and efficacy of the proposed formulation.