Displaying similar documents to “Some existence and bifurcation results for solutions of nonlinear Sturm-Liouville eigenvalue problems.”

Some global results for nonlinear Sturm-Liouville problems with spectral parameter in the boundary condition

Ziyatkhan S. Aliyev, Gunay M. Mamedova (2015)

Annales Polonici Mathematici

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We consider nonlinear Sturm-Liouville problems with spectral parameter in the boundary condition. We investigate the structure of the set of bifurcation points, and study the behavior of two families of continua of nontrivial solutions of this problem contained in the classes of functions having oscillation properties of the eigenfunctions of the corresponding linear problem, and bifurcating from the points and intervals of the line of trivial solutions.

On bifurcation intervals for nonlinear eigenvalue problems

Jolanta Przybycin (1999)

Annales Polonici Mathematici

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We give a sufficient condition for [μ-M, μ+M] × {0} to be a bifurcation interval of the equation u = L(λu + F(u)), where L is a linear symmetric operator in a Hilbert space, μ ∈ r(L) is of odd multiplicity, and F is a nonlinear operator. This abstract result provides an elementary proof of the existence of bifurcation intervals for some eigenvalue problems with nondifferentiable nonlinearities. All the results obtained may be easily transferred to the case of bifurcation from infinity. ...

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.