We establish a priori bounds for positive solutions of semilinear elliptic systems of the form { Delta u= g(x, v), in Omega -Delta v= f (x, u), in Omega u &rt; 0, v &rt; 0 in Omega u= v= 0 on partial derivative Omega where Omega is a bounded and smooth domain in R-2. We obtain results concerning such bounds when f and g depend exponentially with respect to u and v.
Semilinear elliptic systems with exponential nonlinearities in two dimensions / D.G. de Figueireido, J.M. do O, B. Ruf. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - 6:2(2006), pp. 199-213.
Semilinear elliptic systems with exponential nonlinearities in two dimensions
B. RufUltimo
2006
Abstract
We establish a priori bounds for positive solutions of semilinear elliptic systems of the form { Delta u= g(x, v), in Omega -Delta v= f (x, u), in Omega u &rt; 0, v &rt; 0 in Omega u= v= 0 on partial derivative Omega where Omega is a bounded and smooth domain in R-2. We obtain results concerning such bounds when f and g depend exponentially with respect to u and v.
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