Recursos de colección
Project Euclid (Hosted at Cornell University Library) (192.320 recursos)
Differential Integral Equations
Differential Integral Equations
Dai, Guowei; Wang, Jun
This paper is devoted to investigate the existence and multiplicity of radial
nodal solutions for the following Dirichlet problem with mean curvature operator
in Minkowski space \begin{eqnarray} \begin{cases} -\text{div} \Big (\frac{\nabla
v}{\sqrt{1-\vert \nabla v\vert^2}} \Big ) = \lambda f(\vert x\vert,v)\,\,
&\text{in}\,\, B_R(0),\\ v=0~~~~~~~~~~~~~~~~~~~~~~\,\,&\text{on}\,\,
\partial B_R(0). \end{cases} \nonumber \end{eqnarray} By bifurcation approach,
we determine the interval of parameter $\lambda$ in which the above problem has
two or four radial nodal solutions which have exactly $n-1$ simple zeros in
$(0,R)$ according to linear/sublinear/ superlinear nonlinearity at zero. The
asymptotic behaviors of radial nodal solutions as $\lambda \to +\infty$ and $n
\to +\infty$ are also studied.
Ma, To Fu; Souza, Thales Maier
This paper is concerned with a class of wave equations with acoustic boundary
condition subject to non-autonomous external forces. Under some general
assumptions, the problem generates a well-posed evolution process. Then, we
establish the existence of a minimal pullback attractor within a universe of
tempered sets defined by the forcing terms. We also, study the upper
semicontinuity of attractors as the non-autonomous perturbation tends to zero.
Our results allow unbounded external forces and nonlinearities with critical
growth.
Sharma, Vandana; Morgan, Jeff
We consider reaction-diffusion systems where some components react and diffuse on
the boundary of a region, while other components diffuse in the interior and
react with those on the boundary through mass transport. We establish criteria
guaranteeing that solutions are uniformly bounded in time.
Bhakta, Mousomi; Mukherjee, Debangana
In this paper, we prove the existence of infinitely many nontrivial solutions of
the following equations driven by a nonlocal integro-differential operator
$\mathcal{L}_K$ with concave-convex nonlinearities and homogeneous Dirichlet
boundary conditions \begin{align*} \mathcal{L}_{K} u + \mu |u|^{q-1}u + \lambda
|u|^{p-1}u &= 0 \quad\mbox{in}\quad \Omega, \\ u&=0
\quad\mbox{in}\quad\mathbb{R}^N\setminus\Omega, \end{align*} where $\Omega$ is a
smooth bounded domain in $ \mathbb R^N $, $N > 2s$, $s\in(0, 1)$, $0 < q
< 1 < p\leq \frac{N+2s}{N-2s}$. Moreover, when $\mathcal{L}_K$ reduces to
the fractional laplacian operator $-(-\Delta)^s $, $p=\frac{N+2s}{N-2s}$,
$\frac{1}{2} (\frac{N+2s}{N-2s}) < q < 1$, $N > 6s$, $ \lambda =1$, we
find $\mu^*>0$ such that for any $\mu\in(0,\mu^*)$, there exists at least one
sign...
Green, William R.; Toprak, Ebru
We investigate dispersive estimates for the Schrödinger operator $H=-\Delta
+V$ with $V$ is a real-valued decaying potential when there are zero energy
resonances and eigenvalues in four spatial dimensions. If there is a zero energy
obstruction, we establish the low-energy expansion \begin{align*} e^{itH}\chi(H)
P_{ac}(H) & =O(\frac 1{\log t}) A_0+ O(\frac 1 t )A_1+O((t\log t)^{-1})A_2
\\ & + O(t^{-1}(\log t)^{-2})A_3. \end{align*} Here, $A_0,A_1:L^1(\mathbb
R^4)\to L^\infty (\mathbb R^4)$, while $A_2,A_3$ are operators between
logarithmically weighted spaces, with $A_0,A_1,A_2$ finite rank operators,
further the operators are independent of time. We show that similar expansions
are valid for the solution operators to Klein-Gordon and wave equations.
Finally, we show that under certain orthogonality conditions,...
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.