Search results for " two-weighted problems"

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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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