Search results for " planar systems"

showing 2 items of 2 documents

Multiplicity of solutions of Dirichlet problems associated with second-order equations in ℝ2

2009

AbstractWe study the existence of multiple solutions for a two-point boundary-value problem associated with a planar system of second-order ordinary differential equations by using a shooting technique. We consider asymptotically linear nonlinearities satisfying suitable sign conditions. Multiplicity is ensured by assumptions involving the Morse indices of the linearizations at zero and at infinity.

General MathematicsDirichlet L-functionasymptotically linear multiplicity second order planar systems Morse indexDirichlet's energyDirichlet integralsymbols.namesakeDirichlet eigenvalueSettore MAT/05 - Analisi MatematicaDirichlet's principleOrdinary differential equationDirichlet boundary conditionsymbolsApplied mathematicsGeneral Dirichlet seriesMathematics
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Sign-preserving solutions for a class of asymptotically linear systems of second-order ordinary differential equations

2022

We study multiplicity of solutions to an asymptotically linear Dirichlet problem associated with a planar system of second order ordinary differential equations. The existence of two sign-preserving component-wise solutions is guaranteed when the Morse indexes of the linearizations at zero and at infinity do not coincide, and one of the asymptotic problems has zero-index. The proof is developed in the framework of topological and shooting methods and it is based on a detailed analysis and characterization of the phase angles in a two-dimensional setting.

Settore MAT/05 - Analisi MatematicaApplied MathematicsAnalysisAsymptotically Linear Planar Systems Sign-preserving Solutions Morse Index Phase Angles
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