We study an abstract second order nonlinear evolution inclusion in a framework of triple spaces. consider time-dependent possibly nonconvex nonsmooth functions and their Clarke subdifferentials operating on the unknown function. First we prove existence weak solution. Then asymptotic behavior sequence solutions when small parameter inertial term tends to zero. that limit function is solution parabolic hemivariational inequality. Finally, give application theorem quasi-static viscoelastic...

We study a new class of elliptic variational-hemivariational inequalities in reflexive Banach spaces. An inequality the is governed by nonlinear operator, convex set constraints and two nondifferentiable functionals, among which at least one convex. deliver result on existence uniqueness solution to inequality. Next, we show continuous dependence data problem introduce penalty method, for state prove convergence result. Finally, consider mathematical model describes equilibrium an elastic...

Purpose The objective of this study was to compare vocabulary size and composition in 2-year-olds learning Polish or English as measured by the Language Development Survey (LDS; Rescorla, 1989). Method Participants were 199 toddlers ( M = 24.14 months, SD 0.35) 422 U.S. 24.69 0.78). Results Test–retest reliability .92, internal consistency .99, concurrent validity .55. Girls had higher scores than boys. Mean LDS score significantly lower English, fewer children >200 words. Also, more...

We consider a class of abstract second-order evolutionary inclusions involving Volterra-type integral term, for which we prove an existence and uniqueness result. The proof is based on arguments with monotone operators the Banach fixed point theorem. Next, apply this result to solvability integrodifferential hemivariational inequalities and, under additional assumption, its unique solvability. Then mathematical model describes frictional contact between deformable body foundation. process...

In this article, we study nonlinear second order evolution inclusions defined on an triple of spaces. First, prove the existence solutions. We introduce integral operator, reduce problem to Cauchy one for a first inclusion and exploit surjectivity result operators which are pseudomonotone with respect domain other linear, densely maximal monotone operator. Then, give application unilateral contact viscoelasticity is modeled by dynamic hemivariational inequality.

We consider a mathematical model which describes the static frictional contact between piezoelectric body and foundation. The material behavior is described with nonlinear electro-elastic constitutive law. novelty of consists in fact that foundation assumed to be electrically conductive both conductivity on surface are subdifferential boundary conditions involve fully coupling mechanical electrical variables. derive variational formulation problem form system two hemivariational inequalities...

We consider an abstract first-order evolutionary inclusion in a reflexive Banach space. The contains the sum of L-pseudomonotone operator and maximal monotone operator. provide existence theorem which is generalization former results known literature. Next, we apply our result to case nonlinear variational–hemivariational inequalities considered setting evolution triple spaces. specify multivalued operators problem obtain for several classes inequality problems. Finally, illustrate treat...

We consider a mathematical model which describes the frictional contact between piezoelectric body and foundation. The material behaviour is modelled with non-linear electro-elastic constitutive law, bilateral, process static foundation assumed to be electrically conductive. Both friction law electrical conductivity condition on surface are described subdifferential boundary conditions. derive variational formulation of problem form system two coupled hemi-variational inequalities for...