Global bifurcation results for some fourth-order nonlinear eigenvalue problem with a spectral parameter in the boundary condition

This paper is devoted to the study of global bifurcation from infinity of nontrivial solutions of a nonlinear eigenvalue problem for ordinary differential equations of fourth order with a spectral parameter in the boundary condition. We prove the existence of two families of unbounded continua of nontrivial solutions to this problem, which emanate from bifurcation points in $ℝ\times \{\infty \}$ and possess oscillatory properties of eigenfunctions (and their derivatives) of the corresponding linear problem in some neighborhoods of these bifurcation points.     

Metrics with Positive Scalar Curvature at Infinity and Localization Algebra

In this paper, the authors give a new proof of Block and Weinberger’s Bochner vanishing theorem built on direct computations in the K-theory of the localization algebra.