Removable isolated singularities for solutions of quasilinear parabolic equations

We have obtained the best possible conditions for removable singularity at the point for solutions of quasilinear parabolic equations of divergent form

Positive solutions to singular non-linear Schrödinger-type equations

We study the existence and nonexistence of positive (super) solutions to a singular quasilinear second-order elliptic equations with structural coefficients from non-linear Kato-type classes. Under certain general assumptions on the behaviour of the coefficient at infinity we construct an entire positive solution in R^N which is bounded above and below by positive constants. An application is given to a non-existence problem in an exterior domain

Dynamical Systems Gradient method for solving nonlinear equations with monotone operators

A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new stopping rule. Numerical experiments show that the proposed stopping rule is efficient. Equations with monotone operators are of interest in many applications.Comment: 2 figure

On compensated compactness for nonlinear elliptic problems in perforated domains

We consider a sequence of Dirichlet problems for a nonlinear divergent operator A: Wm¹(Ωs ) → [Wm¹(Ωs )]* in a sequence of perforated domains Ωs ⊂ Ω.Розглядається послідовність задач Діріхле для нелінійного дивергентного еліптичного оператора A: Wm¹(Ωs)→[Wm¹(Ωs)]* в послідовності перфорованих областей Ωs ⊂

A monotonicity approach to nonlinear Dirichlet problems in perforated domains

Abstract. We study the asymptotic behaviour of solutions to Dirichlet problems in perforated domains for nonlinear elliptic equations associated with monotone operators. The main difference with respect to the previous papers on this subject is that no uniformity is assumed in the monotonicity condition. Under a very general hypothesis on the holes of the domains, we construct a limit equation, which is satisfied by the weak limits of the solutions. The additional term in the limit problem depends only on the local behaviour of the holes, which can be expressed in terms of suitable nonlinear capacities associated with the monotone operator

A capacitary method for the asymptotic analysis of Dirichlet problems for monotone operators

Given a non-linear elliptic equation of monotone type in a bounded open set \u3a9 82 Rn, we prove that the asymptotic behaviour, as j \u2192 1e, of the solutions of the Dirichlet problems corresponding to a sequence (\u3a9j) of open sets contained in \u3a9 is uniquely determined by the asymptotic behaviour, as j \u2192 1e, of suitable non-linear capacities of the sets K \ \u3a9j, where K runs in the family of all compact subsets of \u3a9

Asymptotic behaviour of nonlinear elliptic higher order equations in perforated domains

Consiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome / CNR - Consiglio Nazionale delle RichercheSIGLEITItal