Estimates for the Green function and singular solutions for polyharmonic nonlinear equation
Bachar, Imed ; Mâagli, Habib ; Masmoudi, Syrine ; Zribi, Malek
Abstr. Appl. Anal., Tome 2003 (2003) no. 7, p. 715-741 / Harvested from Project Euclid
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We establish a new form of the $3G$ theorem for polyharmonic Green function on the unit ball of $\mathbb{R}^n (n\geq 2)$ corresponding to zero Dirichlet boundary conditions. This enables us to introduce a new class of functions $K_{m,n}$ containing properly the classical Kato class $K_n$ . We exploit properties of functions belonging to $K_{m,n}$ to prove an infinite existence result of singular positive solutions for nonlinear elliptic equation of order $2m$ .
Publié le : 2003-06-30
Classification:  34B27,  35J40 
@article{1057257795,
     author = {Bachar, Imed and M\^aagli, Habib and Masmoudi, Syrine and Zribi, Malek},
     title = {Estimates for the Green function and singular solutions for polyharmonic nonlinear equation},
     journal = {Abstr. Appl. Anal.},
     volume = {2003},
     number = {7},
     year = {2003},
     pages = { 715-741},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1057257795}
}

Bachar, Imed; Mâagli, Habib; Masmoudi, Syrine; Zribi, Malek. Estimates for the Green function and singular solutions for polyharmonic nonlinear equation. Abstr. Appl. Anal., Tome 2003 (2003) no. 7, pp.  715-741. http://gdmltest.u-ga.fr/item/1057257795/