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nodal lines

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Asymptotic behaviour, nodal lines and symmetry properties forsolutions of superlinear elliptic equations nearan eigenvalue
Dimitri Mugnai
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 11 / Issue 4 / October 2005

Published online by Cambridge University Press:

15 September 2005, pp. 508-521

Print publication:

October 2005
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We give the precise behaviour of some solutions of a nonlinearelliptic B.V.P. in a bounded domain when a parameter approaches aneigenvalue of the principal part. If the nonlinearity has someregularity and the domain is for example convex, we also prove anonlinear version of Courant's Nodal theorem.