Search results for " weighted eigenvalue"

showing 2 items of 2 documents

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
researchProduct

Multiplicity of solutions for asymptotically linear $n$-th order boundary value problems

2007

In this paper we investigate existence and multiplicity of solutions, with prescribed nodal properties, to a two-point boundary value problem of asymptotically linear $n$-th order equations. The proof follows a shooting approach and it is based on the weighted eigenvalue theory for linear $n$-th order boundary value problems

n-th order problem asymptotically linear multiplicity results shooting approach weighted eigenvalues
researchProduct