Four-parameter bifurcation for a -Laplacian system.

Fleckinger, Jacqueline; Pardo, Rosa; de Thélin, François

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Remarks on Krasnoselskii bifurcation theorem

Raffaele Chiappinelli (1989)

Commentationes Mathematicae Universitatis Carolinae

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Bifurcations for a problem with jumping nonlinearities

Lucie Kárná, Milan Kučera (2002)

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A bifurcation problem for the equation $Δ u + λ u - α u^{+} + β u^{-} + g (λ, u) = 0$ in a bounded domain in $^{N}$ with mixed boundary conditions, given nonnegative functions $α, β \in L_{\infty}$ and a small perturbation $g$ is considered. The existence of a global bifurcation between two given simple eigenvalues $λ^{(1)}, λ^{(2)}$ of the Laplacian is proved under some assumptions about the supports of the functions $α, β$ . These assumptions are given by the character of the eigenfunctions of the Laplacian corresponding to $λ^{(1)}, λ^{(2)}$ .