Abstract
We prove a Liouville-type theorem for entire solutions of the elliptic system $-\Delta u = |v|^{q-2}v$, $-\Delta v=|u|^{p-2}u$ having finite relative Morse index in the sense of Abbondandolo. Here, $p,q > 2$ and $1/p+1/q> (N-2)/N$. In particular, this yields a result on a priori bounds in $L^{\infty}\times L^{\infty}$ for solutions of superlinear elliptic systems obtained by means of min-max theorems, for both Dirichlet and Neumann boundary conditions.
Citation
Miguel Ramos. "A priori bounds via the relative Morse index of solutions of an elliptic system." Topol. Methods Nonlinear Anal. 34 (1) 21 - 39, 2009.
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