0000000000313180

AUTHOR

Armands Gritsans

showing 2 related works from this author

Characteristic numbers of non‐autonomous emden‐fowler type equations

2006

We consider the Emden‐Fowler equation x” = ‐q(t)|x|2εx, ε > 0, in the interval [a,b]. The coefficient q(t) is a positive valued continuous function. The Nehari characteristic number An associated with the Emden‐Fowler equation coincides with a minimal value of the functional [] over all solutions of the boundary value problem x” = ‐q(t)|x|2εx, x(a) = x(b) = 0, x(t) has exactly (n ‐ 1) zeros in (a, b). The respective solution is called the Nehari solution. We construct an example which shows that the Nehari extremal problem may have more than one solution. First Published Online: 14 Oct 2010

Pure mathematicsContinuous function (set theory)Mathematical analysisNehari's solutionsValue (computer science)Interval (mathematics)-Type (model theory)Emden‐Fowler equationModeling and SimulationQA1-939Boundary value problemAnalysisCharacteristic numberMathematicsMathematicscharacteristic numbersMathematical Modelling and Analysis
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Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System

2016

We consider the second order system x′′=f(x) with the Dirichlet boundary conditions x(0)=0=x(1), where the vector field f∈C1(Rn,Rn) is asymptotically linear and f(0)=0. We provide the existence and multiplicity results using the vector field rotation theory.

Article SubjectDirichlet conditionslcsh:MathematicsApplied Mathematics010102 general mathematicsMathematical analysisMixed boundary conditionDirichlet's energylcsh:QA1-93901 natural sciences010101 applied mathematicssymbols.namesakeDirichlet eigenvalueGeneralized Dirichlet distributionDirichlet's principleDirichlet boundary conditionsymbolsBoundary value problem0101 mathematicsAnalysisMathematicsInternational Journal of Differential Equations
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