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L’object de ce travail est l’etude des fonctions fonctions localement sommable $\omega$ sur ${𝐑}^n,n\ge 2$, vérifiant ${\Delta }^2\omega \ge 0$ (où $\Delta$ est Laplacien pris au sens des distributions) et que se comportent à l’infini comme des fonctions sousharmoniques. En parculier, nous caractérisons les fonctious qui sont à la fois bi-sousharmoniques et sousharmoniques.

In this paper, we study the Martin boundary associated with a harmonic structure given by a coupled partial differential equations system. We give an integral representation for non negative harmonic functions of this structure. In particular, we obtain such results for biharmonic functions (i.e. ${▵}^2\varphi =0$) and for non negative solutions of the equation ${▵}^2\varphi =\varphi$.

In this paper, we study the reduit, the thinness and the non-tangential limit associated to a harmonic structure given by coupled partial differential equations. In particular, we obtain such results for biharmonic equation (i.e. ${▵}^2\varphi =0$) and equations of ${▵}^2\varphi =\varphi$ type.