Search results for "Duffing system"

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Nonlinear multivalued Duffing systems

2018

We consider a multivalued nonlinear Duffing system driven by a nonlinear nonhomogeneous differential operator. We prove existence theorems for both the convex and nonconvex problems (according to whether the multivalued perturbation is convex valued or not). Also, we show that the solutions of the nonconvex problem are dense in those of the convex (relaxation theorem). Our work extends the recent one by Kalita-Kowalski (JMAA, https://doi.org/10.1016/j.jmaa. 2018.01.067).

RelaxationMathematics::General TopologyPerturbation (astronomy)34A60 34B1501 natural sciencesMathematics - Analysis of PDEsContinuous and measurable selectionNonlinear differential operatorSettore MAT/05 - Analisi MatematicaClassical Analysis and ODEs (math.CA)FOS: Mathematics0101 mathematicsMathematicsApplied Mathematics010102 general mathematicsMathematical analysisRegular polygonFixed pointDifferential operatorDuffing system010101 applied mathematicsNonlinear systemMathematics - Classical Analysis and ODEsAnalysisConvex and nonconvex problemAnalysis of PDEs (math.AP)Journal of Mathematical Analysis and Applications
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Nonlinear vector Duffing inclusions with no growth restriction on the orientor field

2019

We consider nonlinear multivalued Dirichlet Duffing systems. We do not impose any growth condition on the multivalued perturbation. Using tools from the theory of nonlinear operators of monotone type, we prove existence theorems for the convex and the nonconvex problems. Also we show the existence of extremal trajectories and show that such solutions are $C_0^1(T,\mathbb{R}^N)$-dense in the solution set of the convex problem (strong relaxation theorem).

Pure mathematicsApplied MathematicsRegular polygonSolution setPerturbation (astronomy)Dirichlet distributionDuffing systemNonlinear systemsymbols.namesakeMonotone polygonNonlinear operator of mono-tone typeGrowth restrictionSettore MAT/05 - Analisi MatematicaConvex optimizationStrong relaxationssymbolsExtremal solutionAnalysisMathematics
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