Special Issue in honor of Alan C. Lazer. Electron. J. Diff. Eqns., Special Issue 01 (2021), pp. 279-292.

Bifurcation from infinity with oscillatory nonlinearity for Neumann problems

Maya Chhetri, Nsoki Mavinga, Rosa Pardo

We consider a sublinear perturbation of an elliptic eigenvalue problem with Neumann boundary condition. We give sufficient conditions on the nonlinear perturbation which guarantee that the unbounded continuum, bifurcating from infinity at the first eigenvalue, contains an unbounded sequence of turning points as well as an unbounded sequence of resonant solutions. We prove our result by using bifurcation theory combined with a careful analysis of the oscillatory behavior of the continuum near the bifurcation point.

Published January 3, 2022.
Math Subject Classifications: 35B05, 35B40, 35J25.
Key Words: Bifurcation from infinity; oscillatory nonlinearity; turning points; Neumann boundary condition; resonant solutions.

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Maya Chhetri
UNC Greensboro
Greensboro, NC, USA
email: m_chhetr@uncg.edu
Nsoki Mavinga
Swarthmore College
Swarthmore, PA, USA
email: nmaving1@swarthmore.edu
Rosa Pardo
Universidad Complutense de Madrid
Madrid, Spain
email: rpardo@ucm.es

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