Search results for " continuation theorem"

showing 2 items of 2 documents

Multiplicity results for systems of asymptotically linear second order equations

2002

Abstract We prove the existence and multiplicity of solutions, with prescribed nodal properties, for a BVP associated with a system of asymptotically linear second order equations. The applicability of an abstract continuation theorem is ensured by upper and lower bounds on the number of zeros of each component of a solution.

Asymptotically linearAsymptotically linear second order system continuation theoremGeneral MathematicsMultiplicity resultsMathematical analysisSecond order equationStatistical and Nonlinear PhysicsMathematicsAdvanced Nonlinear Studies
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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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