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Factorization of linear and nonlinear differential operators: necessary and sufficient conditions
Mahouton Norbert Hounkonnou, Pascal Dkengne Sielenou
An algebraic approach for factorizing nonlinear partial differential equations (PDEs) and systems of PDEs is provided. In the particular case of second order linear and nonlinear P…
Conservation laws for under determined systems of differential equations
Mahouton Norbert Hounkonnou, Pascal Dkengne Sielenou
This work extends the Ibragimov's conservation theorem for partial differential equations [{\it J. Math. Anal. Appl. 333 (2007 311-328}] to under determined systems of differential…
General second order conditions for extrema of functionals
Mahouton Norbert Hounkonnou, Pascal Dkengne Sielenou
We prove both necessary and sufficient second order conditions of extrema for variational problems involving any higher order continuously twice differentiable Lagrangians with mul…