8,205 research outputs found
Isospectral deformations of the Dirac operator
We give more details about an integrable system in which the Dirac operator
D=d+d^* on a finite simple graph G or Riemannian manifold M is deformed using a
Hamiltonian system D'=[B,h(D)] with B=d-d^* + i b. The deformed operator D(t) =
d(t) + b(t) + d(t)^* defines a new exterior derivative d(t) and a new Dirac
operator C(t) = d(t) + d(t)^* and Laplacian M(t) = d(t) d(t)^* + d(t)* d(t) and
so a new distance on G or a new metric on M.Comment: 32 pages, 8 figure
Existence of Nontrivial Solutions for p-Laplacian Equations in {R}^{N}
In this paper, we consider a p-Laplacian equation in {R}^{N}with
sign-changing potential and subcritical p-superlinear nonlinearity. By using
the cohomological linking method for cones developed by Degiovanni and
Lancelotti in 2007, an existence result is obtained. We also give a result on
the existence of periodic solutions for one-dimensional -Laplacian equations
which can be proved by the same method.Comment: 19 pages, submitte
Highly oscillatory solutions of a Neumann problem for a -laplacian equation
We deal with a boundary value problem of the form where for and , and is a
double-well potential. We study the limit profile of solutions when and, conversely, we prove the existence of nodal solutions associated
with any admissible limit profile when is small enough
Infinitely many periodic solutions for a class of fractional Kirchhoff problems
We prove the existence of infinitely many nontrivial weak periodic solutions
for a class of fractional Kirchhoff problems driven by a relativistic
Schr\"odinger operator with periodic boundary conditions and involving
different types of nonlinearities
Periodic solutions of forced Kirchhoff equations
We consider Kirchhoff equations for vibrating bodies in any dimension in
presence of a time-periodic external forcing with period 2pi/omega and
amplitude epsilon, both for Dirichlet and for space-periodic boundary
conditions.
We prove existence, regularity and local uniqueness of time-periodic
solutions of period 2pi/omega and order epsilon, by means of a Nash-Moser
iteration scheme. The results hold for parameters (omega, epsilon) in Cantor
sets having measure asymptotically full as epsilon tends to 0.
(What's new in version 2: the case of finite-order Sobolev regularity, the
case of space-periodic boundary conditions, a different iteration scheme in the
proof, some references).Comment: 23 page
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