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| Using Leray-Schauder degree arguments, existence results for positive solutions are proved for ordinary differential systems of the form
$$\eta(r ) [r^{n-1}(A - A^0(r ))']'+ r^{n-1}[-A + A^0(r ) + N f(r,A)] = 0,$$
$$(r^{n-1}N')' + [r^{n-1}g(r,A,A')N]' - r^{n-1}\omega^2(N-1) = 0,$$
with Neumann boundary conditions on $[l,L]$, coming from the study of radial solutions in an annulus of elliptic systems coming from some model for the burglary of houses. The requested a priori estimates are obtained by some unusual combination of pointwise and $L^1$-estimates. |
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