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TOPOLOGICAL METHODS
IN
NONLINEAR ANALYSIS
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| Vol. 31, No. 1 March 2008 |
TABLE OF CONTENTS
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Title and Author(s) |
Page |
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A bifurcation result of Böhme-Marino type for quasilinear elliptic equations
Elisabetta Benincasa and Annamaria Canino
| ABSTRACT.
We study a variational bifurcation problem of
Bohme-Marino type associated with nonsmooth functional. The
existence of two branches of bifurcation is proved.
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1
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Multiplicity results for superquadratic Dirichlet boundary value problems in R^2
Anna Capietto and Walter Dambrosio
| ABSTRACT.
In this paper it is studied the Dirichlet problem associated to the planar
system $z'=J\nabla F(t,z)$. We consider the situation where the Hamiltonian
$F$ satisfies a superquadratic-type condition at infinity.
By means of a bifurcation argument we prove the existence
of infinitely many solutions. These solutions are distinguished
by the Maslov index of an associated linear system.
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19
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On the structure of the solution set for a class of nonlinear equations involving a duality mapping
George Dinca and Mohamed Rochdi
| ABSTRACT.
Sufficient conditions ensuring that the solution set of some operator
equations involving a duality mapping is non-empty, compact and convex
are given.
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29
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Attractors for semilinear damped wave equations on arbitrary unbounded domains
Martino Prizzi and Krzysztof P. Rybakowski
ABSTRACT.
We prove existence of global attractors for semilinear
damped wave equations of the form
\eps u_{tt}+\alpha(x)
u_t+\beta(x)u- \sum_{ij}(a_{ij}(x) u_{x_j})_{x_i}&\,=f(x,u),\quad x\in \Omega,\,t\in\ro0,\infty..,
u(x,t)&\,=0,&\quad& x\in \partial \Omega,\ t\in\ro0,\infty...
on an unbounded domain $\Omega$, without
smoothness assumptions on $\beta(\,\cdot\,)$,
$a_{ij}(\,\cdot\,)$, $f(\,\cdot\,,u)$ and
$\partial\Omega$, and $f(x,\,\cdot\,)$ having critical or subcritical growth.
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49
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A multiplicity result for a semilinear Maxwell type equation
Antonio Azzollini
| ABSTRACT.
In this paper we look for solutions of the equation
\delta d\A=f'(\langle\A,\A\rangle)\A\quad \text{in }\R^{2k},
where $\A$ is a $1$-differential form and $k\geq 2$. These solutions
are critical points of a functional which is strongly indefinite
because of the presence of the differential operator $\delta d.$
We prove that, assuming a suitable convexity condition on the
nonlinearity, the equation possesses infinitely many finite energy
solutions.
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83
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Oscillation and concentration effects described by Young measures which control discontinuous functions
Agnieszka Kałamajska
| ABSTRACT.
We study oscillation and concentration effects for
sequences of compositions $\{ f(u^\nu)\}_{\nu\in\n}$ of
$\mu$-measurable functions $u^\nu\colon \Omega\rightarrow\Rom$ where
$\Omega$ is the compact subset of $\r^n$
and $f$ is
the (possibly) discontinuous function.
The limits are described in terms of Young measures which can
control discontinuous functions recently introduced in \cite{14}.
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111
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The proof of the continuation property of the Conley index over a phase space
Jacek Szybowski
| ABSTRACT.
We prove the continuation property of the Conley index over a
phase space for discrete semidynamical systems.
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139
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Jiang-type theorems for coincidences of maps into homogeneous spaces
Daniel Vendruscolo and Peter Wong
| ABSTRACT.
Let $f,g\colon X\to G/K$ be maps from a closed connected orientable
manifold $X$ to an orientable coset space $M=G/K$ where $G$ is
a compact connected Lie group, $K$ a closed subgroup and $\dim X=\dim M$.
In this paper, we show that if $L(f,g)=0$ then $N(f,g)=0$; if $L(f,g)\ne 0$
then $N(f,g)=R(f,g)$ where $L(f,g), N(f,g)$, and $R(f,g)$ denote the Lefschetz,
Nielsen, and Reidemeister coincidence numbers of $f$ and $g$, respectively.
When $\dim X> \dim M$, we give conditions under which $N(f,g)=0$ implies $f$
and $g$ are deformable to be coincidence free.
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151
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Remarks to the orientation and homotopy in coincidence problems involving Fredholm operators of nonnegative index
Dorota Gabor
| ABSTRACT.
We introduce a notion of orientation of a Fredholm
operators of nonnegative index and use it in a generalized
homotopy property of the respective coincidence index.
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161
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On deterministic and Kolmogorov extensions for topological flows
Brunon Kamiński, Artur Siemaszko and Jerzy Szymański
| ABSTRACT.
The concepts of deterministic and Kolmogorov extensions of topological
flows are introduced. We show that the class of deterministic extensions
contains distal extensions and moreover that for the deterministic extensions
the relative topological entropy vanishes and hence they preserve
the topological entropy. On the other hand we relate the Kolmogorov
extensions to the asymptotic ones and we show that the class of these
extensions contains uniquely ergodic u.p.e. extensions and also the
class of flows admitting an invariant relative $K$-measure with full support.
The main tool used to get these results is the relative version
of the Rokhlin--Sinai theorem concerning the existence of perfect
measurable partitions.
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191
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