The index at infinity for some vector fields with oscillating nonlinearities
(2000) Discrete and Continuous Dynamical Systems —
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- Abstract
- This paper is devoted to the computation of the index at infinity for some asymptotically linear completely continuous vector fields a:-T(a:), when the principal linear part x - Ax is degenerate (1 is an eigenvalue of A), and the sublinear part is not asymptotically homogeneous (in particular do not satisfy Landesman-Lazer conditions). In this work we consider only the case of a one-dimensional degeneration of the linear part, i.e.s 1 is a simple eigenvalue of A. For this case we formulate an abstract theorem and give some general examples for vector fields of Hammerstein type and for a two point boundary value problem.
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Krasnosel’skii, A., & Mawhin, J. (2000). The index at infinity for some vector fields with oscillating nonlinearities. Discrete and Continuous Dynamical Systems. https://hdl.handle.net/2078.5/42932