We give sufficient conditions for non-existence of positive solutions of the equation Δu + a(x)u + b(x)up = 0 on a cone of ℝn We further analyze the existence of positive solutions in the radial, subcritical case, and show that under suitable conditions on the coefficients, every radial solution whose value in 0 is sufficiently large must vanish. 2000 Mathematics Subject Classification: Primary: 35J60 Secondary: 35B05, 35R45.
A Liouville theorem for a class of superlinear elliptic equations on cones / Marco Rigoli, Alberto G. Setti. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - 9:1(2002), pp. 15-36.
A Liouville theorem for a class of superlinear elliptic equations on cones
Marco Rigoli;
2002
Abstract
We give sufficient conditions for non-existence of positive solutions of the equation Δu + a(x)u + b(x)up = 0 on a cone of ℝn We further analyze the existence of positive solutions in the radial, subcritical case, and show that under suitable conditions on the coefficients, every radial solution whose value in 0 is sufficiently large must vanish. 2000 Mathematics Subject Classification: Primary: 35J60 Secondary: 35B05, 35R45.
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