Infinitely Many Stability Switches in a Problem with Sublinear Oscillatory Boundary Conditions |
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Authors: | Alfonso Castro Rosa Pardo |
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Institution: | 1.Department of Mathematics,Harvey Mudd College,Claremont,USA;2.Departamento de Matemática Aplicada,Universidad Complutense de Madrid,Madrid,Spain |
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Abstract: | We consider the elliptic equation \(-\Delta u +u =0\) with nonlinear boundary condition \(\frac{\partial u}{\partial n}= \lambda u + g(\lambda ,x,u), \) where \(\frac{g(\lambda ,x,s)}{s} \rightarrow 0, \hbox { as }|s|\rightarrow \infty \) and g is oscillatory. We provide sufficient conditions on g for the existence of unbounded sequences of stable solutions, unstable solutions, and turning points, even in the absence of resonant solutions. |
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