0000000000704494

AUTHOR

Fabio Zanolin

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Multiplicity results for asymptotically linear equations, using the rotation number approach

2007

By using a topological approach and the relation between rotation numbers and weighted eigenvalues, we give some multiplicity results for the boundary value problem u′′ + f(t, u) = 0, u(0) = u(T) = 0, under suitable assumptions on f(t, x)/x at zero and infinity. Solutions are characterized by their nodal properties.

Asymptotically linearGeneral MathematicsMultiplicity resultsmedia_common.quotation_subjectMathematical analysisZero (complex analysis)InfinityBoundary value problem continuation theorem shooting without uniqueness rotation number Sturm–Liouville Theory weighted eigenvalue multiplicity resultBoundary value problemRotation (mathematics)Eigenvalues and eigenvectorsRotation numberMathematicsmedia_common
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