Search results for " asymptotically linear"

showing 3 items of 3 documents

A Multiplicity result for a class of strongly indefinite asymptotically linear second order systems

2010

We prove a multiplicity result for a class of strongly indefinite nonlinear second order asymptotically linear systems with Dirichlet boundary conditions. The key idea for the proof is to bring together the classical shooting method and the Maslov index of the linear Hamiltonian systems associated to the asymptotic limits of the given nonlinearity.

Class (set theory)Pure mathematicsApplied MathematicsMathematical analysisLinear systemMultiplicity (mathematics)34B15 37J05 53C50Functional Analysis (math.FA)Hamiltonian systemMathematics - Functional AnalysisNonlinear systemsymbols.namesakeShooting methodMathematics - Classical Analysis and ODEsSettore MAT/05 - Analisi MatematicaDirichlet boundary conditionClassical Analysis and ODEs (math.CA)FOS: MathematicssymbolsOrder (group theory)Multiplicity Asymptotically linear BVP Maslov index Phase angleAnalysisMathematics
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Multiplicity results for asymmetric boundary value problems with indefinite weights

2004

We prove existence and multiplicity of solutions, with prescribed nodal properties, to a boundary value problem of the formu″+f(t,u)=0,u(0)=u(T)=0. The nonlinearity is supposed to satisfy asymmetric, asymptotically linear assumptions involving indefinite weights. We first study some auxiliary half-linear, two-weighted problems for which an eigenvalue theory holds. Multiplicity is ensured by assumptions expressed in terms of weighted eigenvalues. The proof is developed in the framework of topological methods and is based on some relations between rotation numbers and weighted eigenvalues.

lcsh:MathematicsApplied MathematicsMultiplicity resultsMathematical analysis34B15Of the formMultiplicity (mathematics)Mixed boundary conditionlcsh:QA1-939Asymmetric boundary value problem asymptotically linear two-weighted problems eigenvalue theory topological methods rotation number multiplicity resultFree boundary problemBoundary value problemAnalysisMathematicsAbstract and Applied Analysis
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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
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