6533b834fe1ef96bd129d735

RESEARCH PRODUCT

Existence and Relaxation Results for Second Order Multivalued Systems

Calogero VetroNikolaos S. Papageorgiou

subject

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 mathematicsMathematics

description

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.

yearjournalcountryeditionlanguage
2021-05-04Acta Applicandae Mathematicae
https://doi.org/10.1007/s10440-021-00410-9