On a class of semilinear elliptic systems and applications in polyharmonic equations (Q5930133)

The main object of the paper is the following differential inequality system in \({\mathbb{R}}^n\setminus\{0\}:\) NEWLINE\[NEWLINE\Delta u_1 \geq X_1(x) U_2^ {p_1} ,\dots \Delta u_k \geq X_k(x) U_{k+1}^ { p_k} , U_{k+1}=U_1NEWLINE\]NEWLINE with \(X_j(x)\geq 0, p_j>0\), for \(j=1,2,\cdots,k\) and \(p_1\cdots p_k>1\); \(\Delta\) is the Laplacian in \({\mathbb{R}}^n\). It is shown that under some general assumptions positive solutions of the system are bounded. As an application it is proved that any positive solution of some polyharmonic equations involving critical exponents is a poly-super-harmonic function.