Search results for "Continuous and measurable selection"

showing 2 items of 2 documents

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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Existence and Relaxation Results for Second Order Multivalued Systems

2021

AbstractWe consider nonlinear systems driven by a general nonhomogeneous differential operator with various types of boundary conditions and with a reaction in which we have the combined effects of a maximal monotone term $A(x)$ A ( x ) and of a multivalued perturbation $F(t,x,y)$ F ( t , x , y ) which can be convex or nonconvex valued. We consider the cases where $D(A)\neq \mathbb{R}^{N}$ D ( A ) ≠ R N and $D(A)= \mathbb{R}^{N}$ D ( A ) = R N and prove existence and relaxation theorems. Applications to differential variational inequalities and control systems are discussed.

RelaxationPure mathematicsPartial differential equationApplied Mathematics010102 general mathematicsMaximal monotone mapOrder (ring theory)Differential operator01 natural sciencesOptimal control010101 applied mathematicsNonlinear systemMonotone polygonSettore MAT/05 - Analisi MatematicaContinuous and measurable selectionsVariational inequalityConvex and nonconvex problemsRelaxation (physics)Boundary value problem0101 mathematicsMathematicsActa Applicandae Mathematicae
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