1,721,014 research outputs found
Multiplicity of homoclinic solutions for a class of asymptotically periodic second order Hamiltonian systems
No full textExistence and multiplicity of homoclinic solutions for a class of asymptotically periodic second order Hamiltonian systems
No full text
Brake orbits type solutions to some class of semilinear elliptic equations
No full textWe consider a class of
semilinear elliptic equations of the form
where is a periodic, positive function and
is modeled on the classical two well Ginzburg-Landau
potential . We show, via variational methods, that
if the set of solutions to the one dimensional heteroclinic problem
has a discrete structure, then
the equation has infinitely many solutions periodic in the variable
and verifying the
asymptotic conditions as
uniformly with respect to
Layered solutions with multiple asymptotes for non autonomous Allen–Cahn equations in R^{3}
No full textWe consider a class of semilinear elliptic equations of the form
\begin{equation}\label{eq:abs}
-\Delta u(x,y,z)+a(x)W'(u(x,y,z))=0,\quad (x,y,z)\in\R^{3},
\end{equation}
where is a periodic, positive, even function and, in the simplest case, is a double well even potential. Under non degeneracy conditions on the set of minimal solutions to the associated one dimensional heteroclinic problem we show, via variational methods the existence of infinitely many geometrically distinct solutions of (\ref{eq:abs}) verifying as uniformly with respect to and such that , in
Multiplicity of entire solutions for a class of almost periodic Allen-Cahn type equations
No full textWe consider a class of
semilinear elliptic equations of the form
where \e>0, is an almost periodic, positive function and
is modeled on the classical two well Ginzburg-Landau
potential . We show via variational
methods that if \e is sufficiently small and is not constant
then the equation admits infinitely many two dimensional entire solutions
verifying the asymptotic conditions as
uniformly with respect to
On global non-degeneracy conditions for chaotic behavior for a class of dynamical systems
No full textFor about 25 years, global methods from the calculus of variations have been used to establish the existence of chaotic behavior for some classes of dynamical systems. Like the analytical approaches that were used earlier, these methods require nondegeneracy conditions, but of a weaker nature than their predecessors. Our goal here is study such a nondegeneracy condition that has proved useful in several contexts including some involving partial differential equations, and to show this condition has an equivalent formulation involving stable and unstable manifolds
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