Liouville theorems for elliptic inequalities and applications. (English) Zbl 0919.35023

Birindelli, Isabeau; Mitidieri, Enzo

Proc. R. Soc. Edinb., Sect. A, Math. 128, No. 6, 1217-1247 (1998).

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.

Reviewer: Marco Biroli (Monza)

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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