Displaying similar documents to “Eigenvalue problems and bifurcation of nonhomogeneous semilinear elliptic equations in exterior strip domains.”

Bifurcation for some semilinear elliptic equations when the linearization has no eigenvalues

Wolfgang Rother (1993)

Commentationes Mathematicae Universitatis Carolinae

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We prove existence and bifurcation results for a semilinear eigenvalue problem in N ( N 2 ) , where the linearization — has no eigenvalues. In particular, we show that under rather weak assumptions on the coefficients λ = 0 is a bifurcation point for this problem in H 1 , H 2 and L p ( 2 p ) .

Asymptotic behaviour, nodal lines and symmetry properties for solutions of superlinear elliptic equations near an eigenvalue

Dimitri Mugnai (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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We give the precise behaviour of some solutions of a nonlinear elliptic B.V.P. in a bounded domain when a parameter approaches an eigenvalue of the principal part. If the nonlinearity has some regularity and the domain is for example convex, we also prove a nonlinear version of Courant’s Nodal theorem.