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Electronic Journal Of Differential Equations


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.


Bifurcation from infinity, oscillatory nonlinearity, turning points, Neumann boundary condition, resonant solutions

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This work is licensed under a Creative Commons Attribution 4.0 International License.


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