Recursos de colección
Project Euclid (Hosted at Cornell University Library) (191.996 recursos)
Differential Integral Equations
Differential Integral Equations
Balanov, Zalman; Wu, Hao-Pin
In this paper, we propose an equivariant degree based method to
study bifurcation of periodic
solutions (of constant period) in symmetric networks of reversible FDEs.
Such a bifurcation occurs when eigenvalues of linearization move along the
imaginary axis
(without change of stability of the trivial solution and possibly without
$1:k$ resonance).
Physical examples motivating considered settings are related to stationary
solutions to
PDEs with non-local interaction: reversible mixed delay differential equations
(MDDEs)
and integro-differential equations (IDEs). In the case of $S_4$-symmetric
networks
of MDDEs and IDEs, we present exact computations of full equivariant
bifurcation invariants.
Algorithms and computational procedures used in this paper are also
included.
Balanov, Zalman; Wu, Hao-Pin
In this paper, we propose an equivariant degree based method to
study bifurcation of periodic
solutions (of constant period) in symmetric networks of reversible FDEs.
Such a bifurcation occurs when eigenvalues of linearization move along the
imaginary axis
(without change of stability of the trivial solution and possibly without
$1:k$ resonance).
Physical examples motivating considered settings are related to stationary
solutions to
PDEs with non-local interaction: reversible mixed delay differential equations
(MDDEs)
and integro-differential equations (IDEs). In the case of $S_4$-symmetric
networks
of MDDEs and IDEs, we present exact computations of full equivariant
bifurcation invariants.
Algorithms and computational procedures used in this paper are also
included.
Bonanno, Gabriele; Iannizzotto, Antonio; Marras, Monica
By means of nonsmooth critical point theory, we prove existence of three weak
solutions
for an ordinary differential inclusion of Sturm-Liouville type involving a
general set-valued
reaction term depending on a parameter, and coupled with mixed boundary
conditions.
As an application, we give a multiplicity result for ordinary differential
equations involving discontinuous nonlinearities.
Bonanno, Gabriele; Iannizzotto, Antonio; Marras, Monica
By means of nonsmooth critical point theory, we prove existence of three weak
solutions
for an ordinary differential inclusion of Sturm-Liouville type involving a
general set-valued
reaction term depending on a parameter, and coupled with mixed boundary
conditions.
As an application, we give a multiplicity result for ordinary differential
equations involving discontinuous nonlinearities.
Ciesielski, Jakub; Janczewska, Joanna; Waterstraat, Nils
We study the existence of homoclinic type solutions for second order
Lagrangian systems of the type $\ddot{q}(t)-q(t)+a(t)\nabla G(q(t))=f(t)$,
where $t\in \mathbb R$, $q\in\mathbb R^n$, $
a\colon\mathbb R\to\mathbb R$ is a continuous positive
bounded function, $G\colon\mathbb R^n\to\mathbb R$ is a $C^1$-smooth potential
satisfying the Ambrosetti-Rabinowitz superquadratic growth condition
and $f\colon\mathbb R\to\mathbb R^n$
is a continuous bounded square integrable forcing term.
A homoclinic type solution is obtained as limit of $2k$-periodic solutions
of an approximative sequence of second order differential equations.
Ciesielski, Jakub; Janczewska, Joanna; Waterstraat, Nils
We study the existence of homoclinic type solutions for second order
Lagrangian systems of the type $\ddot{q}(t)-q(t)+a(t)\nabla G(q(t))=f(t)$,
where $t\in \mathbb R$, $q\in\mathbb R^n$, $
a\colon\mathbb R\to\mathbb R$ is a continuous positive
bounded function, $G\colon\mathbb R^n\to\mathbb R$ is a $C^1$-smooth potential
satisfying the Ambrosetti-Rabinowitz superquadratic growth condition
and $f\colon\mathbb R\to\mathbb R^n$
is a continuous bounded square integrable forcing term.
A homoclinic type solution is obtained as limit of $2k$-periodic solutions
of an approximative sequence of second order differential equations.
Murcia, Edwin G.; Siciliano, Gaetano
We consider a fractional Schrödinger-Poisson system in the whole space
$\mathbb R^{N}$
in presence of a positive potential and depending on a small positive parameter
$\varepsilon.$ We
show that, for suitably small $\varepsilon$ (i.e., in the ``semiclassical
limit'') the
number of positive solutions is estimated below by the
Ljusternick-Schnirelmann category of the set of minima of the potential.
Murcia, Edwin G.; Siciliano, Gaetano
We consider a fractional Schrödinger-Poisson system in the whole space
$\mathbb R^{N}$
in presence of a positive potential and depending on a small positive parameter
$\varepsilon.$ We
show that, for suitably small $\varepsilon$ (i.e., in the ``semiclassical
limit'') the
number of positive solutions is estimated below by the
Ljusternick-Schnirelmann category of the set of minima of the potential.
Massa, Eugenio; Rossato, Rafael Antônio
We consider an elliptic system of
Hamiltonian type with linear
part
depending on two parameters and a sublinear
perturbation. We obtain
the existence of at least three solutions when the
linear part is near
resonance with the principal eigenvalue, either
from above or from below.
For two of these solutions, we also obtain
information on the sign of its
components.
The system is associated to a strongly indefinite
functional and the solutions
are obtained
trough saddle point theorem, after truncating the
nonlinearity.
Massa, Eugenio; Rossato, Rafael Antônio
We consider an elliptic system of
Hamiltonian type with linear
part
depending on two parameters and a sublinear
perturbation. We obtain
the existence of at least three solutions when the
linear part is near
resonance with the principal eigenvalue, either
from above or from below.
For two of these solutions, we also obtain
information on the sign of its
components.
The system is associated to a strongly indefinite
functional and the solutions
are obtained
trough saddle point theorem, after truncating the
nonlinearity.
Killip, Rowan; Murphy, Jason; Visan, Monica; Zheng, Jiqiang
We consider the focusing cubic
nonlinear Schrödinger equation
with inverse-square potential in three space
dimensions. We identify a sharp
threshold between scattering and blowup,
establishing a result analogous to that
of Duyckaerts, Holmer, and Roudenko for the
standard focusing cubic NLS
[7, 11]. We also prove failure of uniform
space-time bounds at the
Killip, Rowan; Murphy, Jason; Visan, Monica; Zheng, Jiqiang
We consider the focusing cubic
nonlinear Schrödinger equation
with inverse-square potential in three space
dimensions. We identify a sharp
threshold between scattering and blowup,
establishing a result analogous to that
of Duyckaerts, Holmer, and Roudenko for the
standard focusing cubic NLS
[7, 11]. We also prove failure of uniform
space-time bounds at the
Iturriaga, Leonelo; Lorca, Sebastián; Massa, Eugenio
In this paper, we consider the quasilinear elliptic
equation $-\Delta_m u=\lambda f(u)$,
in a bounded, smooth and convex domain. When the
nonnegative nonlinearity $f$
has multiple positive zeros, we prove the existence of at
least two positive solutions
for each of these zeros, for $\lambda$ large, without any
hypothesis on the behavior at infinity of $f$.
We also prove a result concerning the behavior of the
solutions as $\lambda\to\infty$.
Sharaf, Khadijah
We consider the following nonlinear elliptic equation
\begin{equation}
\tag{0.1}
A_\frac{1}{2} u = K(x) |u|^{p-1}u \hbox{ in } \Omega, \;\; u=0 \hbox{ on }
\partial\Omega,
\end{equation}
where $\Omega$ is a bounded domain of $\mathbb{R}^n, n\geq 1, K(x)$ is a given
function,
$A_\frac{1}{2}$ represents the square root of $-\Delta$ in $\Omega$ with zero
Dirichlet
boundary condition and $1 < p < \frac{n+1}{n-1}$,
$(p > 1$ if $n=1$). We apply the
Brouwer's fixed
point theorem to prove that (0.1) has infinitely many distinct solutions.
Ambrosio, Vincenzo
We prove the existence of a ground state solution for the following fractional
scalar field equation
\begin{align*}
(-\Delta)^{s} u= g(u) \mbox{ in } \mathbb R^{N}
\end{align*}
where $s\in (0,1)$, $N> 2s$, $(-\Delta)^{s}$ is the fractional Laplacian, and
$g\in C^{1, \beta}( \mathbb R, \mathbb R)$ is an odd function satisfying the critical growth
assumption.
Fan, Jishan; Ozawa, Tohru
We show some regularity criteria for Navier-Stokes equations, the harmonic heat
flow, two liquid crystals models,
and a model for magneto-elastic materials. The method of proof depends on a
systematic use of
interpolation inequalities in Besov spaces and is independent on logarithmic
inequalities.
Zhong, Sijia
In this paper, we will use a gauge transform to prove the local
existence and uniqueness of the derivative nonlinear Schrödinger
equation with additive noise, showing that for the initial data $u_0\in
H^\frac{1}{2}(\mathbb{R})$, there is a local and unique solution almost surely.
Conti, Monica; Gatti, Stefania; Miranville, Alaine
Our aim, in this paper, is to study a generalization of the Caginalp phase-field
system based on the Gurtin--Pipkin law with two temperatures for heat conduction with memory. In particular, we obtain well-posedness results and study the dissipativity, in
terms of the global attractor with optimal regularity, of the associated solution operators. We also study the stability of the system as the memory kernel collapses to a Dirac
mass.
Maryani, Sri; Saito, Hirokazu
The aim of this paper is to show the existence of
$\mathcal{R}$-bounded solution operator families for
two-phase Stokes resolvent equations in
$\dot\Omega =\Omega _+\cup\Omega _-$,
where $\Omega _\pm$ are uniform $W_r^{2-1/r}$
domains of $N$-dimensional Euclidean space
${\mathbf{R}^N}$ ($N\geq 2$, $N < r < \infty$).
More precisely, given a uniform $W_r^{2-1/r}$
domain $\Omega $ with two boundaries $ \Gamma _\pm$
satisfying $ \Gamma _+\cap \Gamma _-=\emptyset$,
we suppose that some hypersurface $ \Gamma $
divides $\Omega $ into two sub-domains, that is,
there exist domains $\Omega _\pm\subset\Omega $ such that
$
\Omega _+\cap\Omega _-=\emptyset$ and $\Omega \setminus \Gamma =\Omega _+\cup\Omega _-,
$
where $ \Gamma \cap \Gamma _+=\emptyset$,
$ \Gamma \cap \Gamma _-=\emptyset$, and the boundaries of
$\Omega _\pm$...
Kobayasi, Kazuo; Noboriguchi, Dai
In this paper, we discuss the Cauchy problem for a degenerate parabolic-hyperbolic equation with a multiplicative noise.
We focus on the existence of a solution. Using nondegenerate smooth approximations, Debussche, Hofmanová and Vovelle
[8] proved the existence of a kinetic solution. On the other hand, we propose to construct a sequence of approximations by applying a time splitting method and
prove that this converges strongly in $L^1$ to a kinetic solution. This method will somewhat give us not only a simpler and more direct argument but an
improvement over the existence result.