Displaying similar documents to “Four-parameter bifurcation for a p -Laplacian system.”

Bifurcations for a problem with jumping nonlinearities

Lucie Kárná, Milan Kučera (2002)

Mathematica Bohemica

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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 ∈ L ∞ 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 ) .

Sharp estimates for the Ambrosetti-Hess problem and consequences

José Gámez, Juan Ruiz-Hidalgo (2006)

Journal of the European Mathematical Society

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Motivated by [3], we define the “Ambrosetti–Hess problem” to be the problem of bifurcation from infinity and of the local behavior of continua of solutions of nonlinear elliptic eigenvalue problems. Although the works in this direction underline the asymptotic properties of the nonlinearity, here we point out that this local behavior is determined by the global shape of the nonlinearity.