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| In this talk, we investigate the following type of quasilinear elliptic system $({\rm P})$ with explosive boundary conditions on a smooth and bounded domain :
$$\Delta_p u=f_1(x,u,v)\quad\text{in }\Omega\, ;\quad u|_{\partial\Omega}=+\infty,\quad u>0\quad\text{in }\Omega,$$
$$\Delta_q v=f_2(x,u,v)\quad\text{in }\Omega\, ;\quad v|_{\partial\Omega}=+\infty,\quad v>0\quad\text{in }\Omega.$$
Under suitable conditions on $f_1$ and $f_2$, we first give a general result relating the existence of large solutions to $({\rm P})$ to the existence of a sub and supersolutions pair to $({\rm P})$. Next, we give some applications considering particular systems arising in Biology. |
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