| Title and Author(s) |
Page |
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Multiple solitary wave solutions of nonlinear Schrodinger systems
Rushun Tian and Zhi-Qiang Wang
ABSTRACT.
Consider the $N$-coupled nonlinear elliptic system
\cases
\displaystyle
-\Delta U_j+ U_j=\mu U_j^3+\beta U_j\sum_{k\neq j} U_k^2
\quad \text{in } \Omega,
U_j>0 \quad\text{in } \Omega,\quad
U_j=0 \quad \text{on } \partial\Omega,\ j=1, \ldots, N.
\endcases
\tag P
where $\Omega$ is a smooth and bounded (or unbounded if $\Omega$ is
radially symmetric) domain in $\R^n$, $n\leq3$. By using
a $Z_N$ index theory, we prove the existence of multiple solutions
of (P) and show the dependence
of multiplicity results on the coupling constant $\beta$.
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203
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Eight positive periodic solutions to tree species non-autonomous Lotka-Volterra cooperative systems with harvesting terms
Yongkun Li and Kaihong Zhao
| ABSTRACT.
By using Mawhin's continuation theorem of coincidence degree theory
and linear inequality, we establish the existence of eight positive
periodic solutions for three species non-autonomous Lotka-Volterra
cooperative systems with harvesting terms. An example is given to
illustrate the effectiveness of our results.
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225
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Existence of periodic solutions for $p$-Laplacian neutral functional equation with multiple deviating
arguments
Tian Xiang and Rong Yuan
| ABSTRACT.
By using the theory of coincidence degree and some refined analysis techniques,
we study a general kind of periodic solutions to $p$-Laplacian
neutral functional differential equation with multiple deviating
arguments. A general analysis method to tackle with such equations
is formed. Some new and universal results on the existence of
periodic solutions are obtained, meanwhile, some known results in
the literatures are improved. An example is provided as an
application to our theorems.
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235
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Forced oscillations in strongly damped beam equation
Aleksander Cwiszewski
| ABSTRACT.
It is proved that the extensible beam equation in Ball's model
admits periodic solutions near equilibrium states if subject
to external periodic force of high frequency.
The approach is based on translation along trajectories, averaging method
and homotopy invariants such as topological degree and fixed point index.
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259
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Unbounded connected component of the positive solutions set of some semi-positone problems
Xu Xian and Sun Jingxian
| ABSTRACT.
In this paper, first we obtain some
results for structure of positive solutions set of some nonlinear
operator equation. Then using these results, we obtain some
existence results for positive solutions of the nonlinear operator
equation. The method to show our main results is the global
bifurcation theory.
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283
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On second-order boundary value problems in Banach spaces: a bound sets approach
Jan Andres, Luisa Malaguti and Martina Pavlackova
| ABSTRACT.
The existence and localization of strong (Carath\'{e}odory) solutions
is obtained for a second-order Floquet problem in a Banach space.
The combination of applied degree arguments and bounding (Liapunov-like)
functions allows some solutions to escape from a given set. The problems
concern both semilinear differential equations and inclusions. The main
theorem for upper-Carath\'{e}odory inclusions is separately improved
for Marchaud inclusions (i.e. for globally upper semicontinuous
right-hand sides) in the form of corollary. Three illustrative examples
are supplied.
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303
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Long time existence of solutions to 2D Navier-Stokes equations with inflow-outflow and heat convection
Piotr Kacprzyk
| ABSTRACT.
Global existence of regular solutions to the Navier-Stokes
equations for velocity and pressure coupled with the heat convection equation
for temperature in cylindrical pipe with inflow and outflow in the
two-dimensional case is shown. We assume the slip boundary conditions for
velocity and the Neumann condition for temperature. First an appropriate
estimate is shown and next the existence of solutions is proved by the
Leray-Schauder fixed point theorem.
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343
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Robustness of nonuniform polynomial dichotomies for difference equations
Luis Barreira, Meng Fan, Claudia Valls and Jimin Zhang
| ABSTRACT.
For a nonautonomous dynamics with discrete time defined by
a sequence of linear operators in a Banach space, we establish
the robustness of polynomial contractions and of polynomial dichotomies
under sufficiently small linear perturbations. In addition, we consider
the general case of nonuniform polynomial behavior.
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357
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Maps on bouquets of circles can be deformed to be coincidence-free
P. Christopher Staecker
| ABSTRACT.
We give a construction to remove coincidence points of continuous maps
on graphs ($1$-complexes) by changing the maps by homotopies. When the
codomain is not homeomorphic to the circle, we show that any pair of
maps can be changed by homotopies to be coincidence free.
This means that there can
be no nontrivial coincidence index, Nielsen coincidence number, or coincidence
Reidemeister trace in this setting, and the results of our
previous paper ``A formula for the coincidence Reidemeister trace of
selfmaps on bouquets of circles'' are invalid.
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377
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Fixed points of hemi-convex multifunctions
Shahram Rezapour, S. M. A. Aleomraninejad and Naaser Shahzad
| ABSTRACT.
The notion of hemi-convex multifunctions is introduced. It is shown
that each convex multifunction is hemi-convex, but the converse is not true.
Some fixed point results for hemi-convex multifunctions are also proved.
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383
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