| Title and Author(s) |
Page |
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An Application of Nonsmooth Critical Point Theory
Li Zhouxin, Shen Yaotian and Zhang Yumin
| ABSTRACT.
We consider a class of elliptic equation with natural growth.
We obtain a region of the
natural growth term with precise lower boundary
less than zero.
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203
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Averaging method for neutral differential equations in finite dimension
Jean-Francois Couchouron and Mikhail I. Kamenskii
| ABSTRACT.
We prove in this paper a periodic existence theorem for neutral differential
equations in finite dimension with high frequency terms. This study completes
previous works about
applications of averaging methods to periodic problems.
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221
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Existence and multiplicity of solutions for resonant nonlinear Neumann problems
Sergiu Aizicovici, Nikolaos S. Papageorgiou and Vasile Staicu
| ABSTRACT.
We consider nonlinear Neumann problems driven by the $p$-Laplacian
differential operator with a Caratheodory nonlinearity. Under hypotheses which
allow resonance with respect to the principal eigenvalue $\lambda_{0}$ $=0$ at
$\pm\infty$, we prove existence and multiplicity results. Our approach is
variational and uses critical point theory and Morse theory (critical groups).
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235
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Nonlinear scalar field equations in R^N: mountain pass and symmetric mountain pass approaches
Jun Hirata, Norihisa Ikoma and Kazunaga Tanaka
ABSTRACT.
We study the existence of radially symmetric solutions of the following
nonlinear scalar field equations in $\R^N$:
-\Delta u=g(u) \quad \text{in }\R^N,
u\in H^1(\R^N).
We give an extension of the existence results due to
H. Berestycki, T. Gallou\"et and O. Kavian \cite{2}.
We take a mountain pass approach in $H^1(\R^N)$ and introduce
a new method generating
a Palais-Smale sequence with an additional property related
to Pohozaev identity.
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253
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Dynamics of the modified viscous Cahn-Hilliard equation in R^N
Tomasz Dlotko and Chunyou Sun
| ABSTRACT.
Global solvability and dynamical behaviour of the modified viscous
Cahn-Hilliard equation is studied in the Sobolev space
$H^1({\Bbb R}^N)$. For $\nu \in [0,1]$ we
construct $H^1({\Bbb R}^N)$ global attractors
and show their upper semicontinuity at $\nu = 0$.
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277
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Existence of solutions for anti-periodic boundary value problems involving fractional differential equations via Leray-Schauder degree theory
Bashir Ahmad and Juan J. Nieto
| ABSTRACT.
In this paper, some existence results for a differential equation
of fractional order with anti-periodic boundary conditions are
presented. The main tool of study is Leray-Schauder degree theory.
|
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295
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Nonconvex perturbations of second order maximal monotone differential inclusions
Dalila Azzam-Laouir and Sabrina Lounis
| ABSTRACT.
In this paper we prove the
existence of solutions for a two point boundary value problem for
a second order differential inclusion governed by a maximal monotone
operator with a mixed semicontinuous
perturbation
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305
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Positive solutions of singularly perturbed nonlinear elliptic problem on Riemannian manifolds with boundary
Marco Ghimenti and Anna Maria Micheletti
ABSTRACT.
Let $(M,g)$ be a smooth connected compact Riemannian manifold of finite
dimension $n\geq 2$\ with a smooth boundary $\partial M$. We consider the
problem
\cases
-\varepsilon ^{2}\Delta _{g}u+u=|u|^{p-2}u,\quad u>0 &\text{ on }M,
\displaystyle
\frac{\partial u}{\partial \nu }=0 & \text{on }\partial M,
\endcases
where $\nu $ is an exterior normal to $\partial M$.
The number of solutions of this problem depends on the topological
properties of the manifold. In particular we consider the Lusternik
Schnirelmann category of the boundary
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319
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Genericity of nondegenerate geodesics with general boundary conditions
Renato G. Bettiol and Roberto Giambo
| ABSTRACT.
Let $M$ be a possibly noncompact manifold. We prove, generically
in the $C^k$-topology ($2\leq k\leq \infty$), that semi-Riemannian
metrics of a given index on $M$ do not possess any degenerate geodesics
satisfying suitable boundary conditions. This extends a result
of L. Biliotti, M. A. Javaloyes and P. Piccione \cite{6}
for geodesics
with fixed endpoints to the case where endpoints lie on a compact
submanifold $\p\subset M\times M$ that satisfies an admissibility
condition. Such condition holds, for example, when $\p$ is transversal
to the diagonal $\Delta\subset M\times M$. Further aspects of these boundary
conditions are discussed and general conditions under which metrics without
degenerate geodesics are $C^k$-generic are given.
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339
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Nontrivial Solutions of p-Superlinear Anisotropic p-Laplacian Systems via Morse Theory
Kanisha Perera, Ravi P. Agarwal and Donald O'Regan
| ABSTRACT.
We obtain nontrivial solutions of a class of $p$-superlinear
anisotropic $p$-Laplacian systems using Morse theory.
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367
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A Borsuk-type theorem for some classes of perturbed Fredholm maps
Pierluigi Benevieri and Alessandro Calamai
| ABSTRACT.
We prove an odd mapping theorem of Borsuk type for locally
compact perturbations of Fredholm maps of index zero between Banach spaces.
We extend this result to a more general class of perturbations of Fredholm
maps, defined in terms of measure of noncompactness.
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379
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The size of some Critical sets by means of dimension and algebraic $\varphi$-category
Cornel Pintea
| ABSTRACT.
Let $M^n$, $N^n$, $n\geq 2$, be compact connected manifolds. We first observe
that mappings of zero degree have high dimensional critical sets and show
that the only possible degree is zero for maps $f\colon M\to N$, under
the assumption on the index $[\pi_1(N):\Im(f_*)]$ to be infinite.
By contrast with the described situation one shows, after some estimates
on the algebraic $\varphi$-category of some pairs of finite groups, that
a critical set of smaller dimension keeps the degree away from zero.
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395
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