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Liouville theorems for elliptic inequalities and applications. (English) Zbl 0919.35023
The authors prove results on nonexistence of $$C^2$$ solutions to systems of semilinear elliptic polyharmonic inequalities in cones or, under better conditions on the nonlinearity, of bounded positive solutions to semilinear elliptic equations in half spaces. Using the previous results a blow-up argument allows to prove a priori bounds for solutions of a class of semilinear elliptic systems in bounded domains.

##### MSC:
 35B45 A priori estimates in context of PDEs 35J60 Nonlinear elliptic equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
##### Keywords:
nonexistence; bounded positive solutions
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##### References:
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