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On nonhomogeneous reinforcements of varying shape and different exponents

Mohamed Boutkrida, Jacqueline Mossino, Gonoko Moussa (1999)

Bollettino dell'Unione Matematica Italiana

Studiamo un problema ellittico quasilineare concernente un dominio circondato da un rinforzo sottile di spessore variabile, in cui il coefficiente dell'equazione è (localmente) non costante. Esso concerne due diversi esponenti, uno nel dominio e l'altro nel rinforzo, una condizione di Dirichlelet sulla frontiera esterna e una condizione di trasmissione. Prediciamo il comportamento asintotico della soluzione quando lo spessore, insieme con il coefficiente nel rinforzo, tende a zero perché essi siano...

On nonlinear, nonconvex evolution inclusions

Nikolaos S. Papageorgiou (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We consider a nonlinear evolution inclusion driven by an m-accretive operator which generates an equicontinuous nonlinear semigroup of contractions. We establish the existence of extremal integral solutions and we show that they form a dense, G δ -subset of the solution set of the original Cauchy problem. As an application, we obtain “bang-bang”’ type theorems for two nonlinear parabolic distributed parameter control systems.

On nonoscillation of canonical or noncanonical disconjugate functional equations

Bhagat Singh (2000)

Czechoslovak Mathematical Journal

Qualitative comparison of the nonoscillatory behavior of the equations L n y ( t ) + H ( t , y ( t ) ) = 0 and L n y ( t ) + H ( t , y ( g ( t ) ) ) = 0 is sought by way of finding different nonoscillation criteria for the above equations. L n is a disconjugate operator of the form L n = 1 p n ( t ) d d t 1 p n - 1 ( t ) d d t ... d d t · p 0 ( t ) . Both canonical and noncanonical forms of L n have been studied.

On non-overdetermined inverse scattering at zero energy in three dimensions

Roman G. Novikov (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We develop the ¯ -approach to inverse scattering at zero energy in dimensions d 3 of [Beals, Coifman 1985], [Henkin, Novikov 1987] and [Novikov 2002]. As a result we give, in particular, uniqueness theorem, precise reconstruction procedure, stability estimate and approximate reconstruction for the problem of finding a sufficiently small potential v in the Schrödinger equation from a fixed non-overdetermined (“backscattering” type) restriction h | Γ of the Faddeev generalized scattering amplitude h in the...

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