1,721,057 research outputs found
Normal geodesics in static spacetimes with critical asymptotic behavior
No full textThis paper deals with the existence of normal geodesics joining two given submanifolds in a static spacetime when the coefficient
of its metric has a quadratic growth. A suitable variational approach allows one to use the classical Ljusternik-Schnirelman theory
Lightlike periodic trajectories in Space-Times
No full textLet be a Lorentz metric on a manifold \m = \mo \times \r such that \mo is not compact. We prove the existence of infinitely many lightlike periodic trajectories in \m by using variational methods and Ljusternik-Schnirelman theory
Multiplicity results for some quasilinear equations in lack of symmetry
No full textIn this paper we prove the existence of multiple nontrivial solutions for the quasilinear equation in divergence form
in an open bounded domain , where
is a given Carathéodory function with
partial derivatives
and .
It generalizes the -Laplacian problem
but, in general, the corresponding functional is not well defined in all the space .
Anyway, under suitable assumptions and by using variational tools, we are able to prove that the number of solutions of depends on the parameter and, even in lack of symmetry, at least three nontrivial solutions exist if is large enough
Normal trajectories in stationary spacetimes with critical asymptotic behavior
No full textThe aim of this note is to study the existence of normal trajectories joining two given submanifolds under the action of an external field in a standard stationary spacetime. Here, it is assumed that both the growth of the potential and that one of the coefficients of the metric are critical in a suitable sense
Periodic solutions for dynamical systems on non-complete Riemannian manifolds
No full textWe look for periodic solutions for a dynamical system on a non-complete
Riemannian manifold. If the potential is bounded and
suitable convexity assumptions hold, the existence of infinitely many solutions can be proved by means of variational methods, penalization arguments and classical Ljusternik-Schnirelman theory
Multiple solitary waves for non-homogeneous Schrödinger-Maxwell equations
No full textThe aim of this paper is investigating the existence of standing waves which are solutions of a nonlinear Schroedinger equation coupled with Maxwell's equations when
a non--homogeneous term breaks the symmetry of the associated functional
Light rays joining two submanifolds in Space-Times
No full textLet \m = \mo \times \Rrset be a stationary Lorentz metric and , be two closed submanifolds of \mo. By using the Ljusternik-Schnirelman theory and variational tools, we prove the influence of the topology of and
on the number of lightlike geodesics in \m joining to P_1 \times \Rrset
Positive solutions for some generalized p–Laplacian type problems
Get PDFIn this paper, we prove the existence of nontrivial weak bounded solutions of the nonlinear elliptic problem{-div(a(x, u, del u)) + A(t)(x, u, del u) = f(x, u) in Omega, u >= 0 in Omega, u = 0 on partial derivative Omega,where Omega subset of R-N is an open bounded domain, N >= 3, and A(x, t, xi), f(x, t) are given functions, with A(t) = partial derivative A/partial derivative t, a = del xi A,To this aim, we use variational arguments which are adapted to our setting and exploit a weak version of the Cerami-Palais-Smale condition.Furthermore, if A(x, t, xi) grows fast enough with respect to t, then the nonlinear term related to f(x, t) may have also a supercritical growth
Soliton solutions for quasilinear modified Schrödinger equations in applied sciences
No full textIn this paper, we prove the existence of nontrivial weak bounded solutions of the quasilinear modified Schrödinger problem
where , are ``good'' functions and is such that
for a given .
By means of variational methods and an approximation argument, here we obtain an existence result for the superfluid film equation in Plasma Physics and for the equation which models the self-channelling of a high-power ultrashort laser,
which derive from our model problem by taking , respectively , in the previous definition of
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