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A weighted symmetrization for nonlinear elliptic and parabolic equations in inhomogeneous media

Guillermo Reyes, Juan Luis Vázquez (2006)

Journal of the European Mathematical Society

In the theory of elliptic equations, the technique of Schwarz symmetrization is one of the tools used to obtain a priori bounds for classical and weak solutions in terms of general information on the data. A basic result says that, in the absence of lower-order terms, the symmetric rearrangement of the solution u of an elliptic equation, that we write u * , can be compared pointwise with the solution of the symmetrized problem. The main question we address here is the modification of the method to...

Abstract inclusions in Banach spaces with boundary conditions of periodic type

Lahcene Guedda, Ahmed Hallouz (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We study in the space of continuous functions defined on [0,T] with values in a real Banach space E the periodic boundary value problem for abstract inclusions of the form ⎧ x ∈ S ( x ( 0 ) , s e l F ( x ) ) ⎨ ⎩ x (T) = x(0), where, F : [ 0 , T ] × → 2 E is a multivalued map with convex compact values, ⊂ E, s e l F is the superposition operator generated by F, and S: × L¹([0,T];E) → C([0,T]; ) an abstract operator. As an application, some results are given to the periodic boundary value problem for nonlinear differential inclusions governed by m-accretive...

Abstract semilinear equations in Banach spaces

Eugenio Sinestrari (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si studiano le proprietà delle soluzioni dell'equazione semilineare astratta u ′ ⁢ ( t ) = Λ ⁢ u ⁢ ( t ) + φ ⁢ ( t , u ⁢ ( t ) ) quando Λ è il generatore infinitesimale di un semigruppo analitico in uno spazio di Banach. Vengono provati nuovi teoremi di regolarità anche nel caso in cui φ non è continuo in tutto lo spazio.

Abstract Subdifferential Calculus and Semi-Convex Functions

Ivanov, Milen, Zlateva, Nadia (1997)

Serdica Mathematical Journal

∗ The work is partially supported by NSFR Grant No MM 409/94.We develop an abstract subdifferential calculus for lower semicontinuous functions and investigate functions similar to convex functions. As application we give sufficient conditions for the integrability of a lower semicontinuous function.

Acceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions

Geoffroy, M., Hilout, S., Pietrus, A. (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 47H04, 65K10.In this paper we investigate the existence of a sequence (xk ) satisfying 0 ∈ f (xk )+ ∇f (xk )(xk+1 − xk )+ 1/2 ∇2 f (xk )(xk+1 − xk )^2 + G(xk+1 ) and converging to a solution x∗ of the generalized equation 0 ∈ f (x) + G(x); where f is a function and G is a set-valued map acting in Banach spaces.

Admissible maps, intersection results, coincidence theorems

Mircea Balaj (2001)

Commentationes Mathematicae Universitatis Carolinae

We obtain generalizations of the Fan's matching theorem for an open (or closed) covering related to an admissible map. Each of these is restated as a KKM theorem. Finally, applications concerning coincidence theorems and section results are given.

Affine-invariant monotone iteration methods with application to systems of nonlinear two-point boundary value problems

Rudolf L. Voller (1992)

Applications of Mathematics

In this paper we present a new theorem for monotone including iteration methods. The conditions for the operators considered are affine-invariant and no topological properties neither of the linear spaces nor of the operators are used. Furthermore, no inverse-isotony is demanded. As examples we treat some systems of nonlinear ordinary differential equations with two-point boundary conditions.

Alcune osservazioni sul rango numerico per operatori non lineari

Jürgen Appell, G. Conti, Paola Santucci (1999)

Mathematica Bohemica

We discuss some numerical ranges for Lipschitz continuous nonlinear operators and their relations to spectral sets. In particular, we show that the spectrum defined by Kachurovskij (1969) for Lipschitz continuous operators is contained in the so-called polynomial hull of the numerical range introduced by Rhodius (1984).

Currently displaying 281 – 300 of 466