共查询到20条相似文献,搜索用时 687 毫秒
1.
Anna Germinario 《Journal of Differential Equations》2007,232(1):253-276
We state a fundamental correspondence between geodesics on stationary spacetimes and the equations of classical particles on Riemannian manifolds, accelerated by a potential and a magnetic field. By variational methods, we prove some existence and multiplicity theorems for fixed energy solutions (joining two points or periodic) of the above described Riemannian equation. As a consequence, we obtain existence and multiplicity results for geodesics with fixed energy, connecting a point to a line or periodic trajectories, in (standard) stationary spacetimes. 相似文献
2.
In this paper we study existence and multiplicity results of geodesics joining two given events in Lorentzian manifolds with
lack of geodesic completeness. The considered Lorentzian manifolds are not necessarily static or stationary and satisfy a
condition of convexity on the boundary.
work supported by M.U.R.S.T. research founds 40%–60% 1992 相似文献
3.
We show that a small neighborhood of a closed symplectic
submanifold in a geometrically bounded aspherical symplectic manifold has
non-vanishing symplectic homology. As a consequence, we establish the existence
of contractible closed characteristics on any thickening of the boundary
of the neighborhood. When applied to twisted geodesic flows on compact
symplectically aspherical manifolds, this implies
the existence of contractible periodic orbits for a dense set of
low energy values. 相似文献
4.
In this paper, two existence results for a class of second order periodic boundary value problems with non-smooth potential are obtained. We extend the Castro-Lazer-Thews reduction method to non-smooth functionals, the obtained result is then exploited to prove the existence of a nontrivial solution. Furthermore, we prove the existence of multiple solutions by using a multiplicity result based on local linking. 相似文献
5.
讨论了时间标度上一类二阶非线性动态方程的周期边值问题正解以及多解的存在性,利用锥上的不动点理论给出了简捷的判别方法并举例。 相似文献
6.
The purpose of this paper is to investigate the multiplicity of solutions for second-order quasilinear periodic boundary value problems with impulsive effects. By using symmetric mountain pass theorem and the genus properties in critical point theory, the existence results of infinitely many solutions are obtained. 相似文献
7.
Xinan Hao Lishan Liu Yonghong Wu 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(9-10):3635-3642
This paper studies the existence of positive solutions for periodic boundary value problems. The criteria for the existence, nonexistence and multiplicity of positive solutions are established by using the Global continuation theorem, fixed point index theory and approximate method. The results obtained herein generalize and complement some previous findings of [J.R. Graef, L. Kong, H. Wang, Existence, multiplicity, and dependence on a parameter for a periodic boundary value problem, J. Differential Equations 245 (2008) 1185–1197] and some other known results. 相似文献
8.
Paolo Secchi 《Mathematical Methods in the Applied Sciences》1997,20(7):583-597
We consider the initial-boundary value problem for quasi-linear symmetric hyperbolic systems with dissipation and characteristic boundary of constant multiplicity. We investigate the global existence and decay property of small regular solutions in suitable functions spaces which take into account the loss of regularity in the normal direction to the characteristic boundary. We also show the existence, uniqueness and stability of the time periodic solutions. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd. 相似文献
9.
Tianqing An 《Journal of Differential Equations》2007,236(1):116-132
Consider the periodic solutions of autonomous Hamiltonian systems on the given compact energy hypersurface Σ=H−1(1). If Σ is convex or star-shaped, there have been many remarkable contributions for existence and multiplicity of periodic solutions. It is a hard problem to discuss the multiplicity on general hypersurfaces of contact type. In this paper we prove a multiplicity result for periodic solutions on a special class of hypersurfaces of contact type more general than star-shaped ones. 相似文献
10.
讨论一阶泛函微分方程的周期边值问题,利用锥上的不动点定理给出了正解的存在性和多重性的简捷的判别条件. 相似文献
11.
The existence and multiplicity of positive solutions are established to periodic boundary value problems for singular nonlinear second order ordinary differential equations. The arguments are based only upon the positivity of the Green's functions and the Krasnosel'skii fixed point theorem. As an example, a periodic boundary value problem is also considered which comes from the theory of nonlinear elasticity. 相似文献
12.
The existence and multiplicity of positive solutions to a periodic boundary value problem for nonlinear third-order ordinary differential equation are established, based on the zero point theorem concerning cone expansion and compression of order type. Our main approach is different from the previous papers on the existence of multiple positive solutions to the similar problem. 相似文献
13.
The existence and multiplicity of positive solutions are established to the periodic boundary value problems for repulsive singular nonlinear difference equations. The proof relies on a nonlinear alternative of Leray–Schauder type and on Krasnoselskii fixed point theorem on compression and expansion of cones. 相似文献
14.
Tianqing An 《Journal of Mathematical Analysis and Applications》2004,295(1):144-152
This paper discusses the existence and multiplicity of periodic orbits of Hamiltonian systems on symmetric positive-type hypersurfaces. We prove that each such energy hypersurface carries at least one symmetric periodic orbit. Under some suitable pinching conditions, we also get an existence result of multiple symmetric periodic orbits. 相似文献
15.
C. Viterbo 《Geometric And Functional Analysis》1999,9(5):985-1033
This paper is concerned with Floer cohomology of manifolds with contact type boundary. In this case, there is no conjecture
on this ring, as opposed to the compact case, where it is isomorphic to the usual cohomology (with the quantum product). We
construct two mappings in Floer cohomology and prove some functorial properties of these two mappings. The first one is a
map from the Floer cohomology of M to the relative cohomology of M modulo its boundary. The other is associated to a codimension zero embedding, and may be considered as a cohomological transfer.
These maps are used to define some properties of symplectic manifolds with contact type boundary. These are algebraic versions
of the Weinstein conjecture, asserting existence of closed characteristics on . This is proved for many cases, Euclidean space and subcritical Stein manifolds, vector bundles, products, cotangent bundles.
It is also proved that the above property implies some restrictions on Lagrangian embeddings, and also yields in certain cases,
existence results for holomorphic curves bounded by the Lagrange submanifold. The last section is devoted to applications
of this existence result, to real forms of Stein manifolds and obstructions to polynomial convexity in Stein manifolds. Many
of our applications rely on the computation of the Floer cohomology of a cotangent bundle, that is the subject of Part II.
Submitted: December 1997, revised version: February 1999. 相似文献
16.
In this paper we study the existence and multiplicity of periodic orbits of exact magnetic flows with energy levels above the Mañé critical value of the universal cover on a non-compact manifold from the viewpoint of Morse theory. 相似文献
17.
Differential Equations - A criterion for the existence of solutions of the second boundary value problem for the $$p $$ -Laplacian on hyperbolic Riemannian manifolds with a model end is obtained. 相似文献
18.
Gabriele Bonanno Giovanni Molica Bisci Vicenţiu D. Rădulescu 《manuscripta mathematica》2013,142(1-2):157-185
The existence of one non-trivial solution for a nonlinear problem on compact d-dimensional ( ${d \geq 3}$ ) Riemannian manifolds without boundary, is established. More precisely, a recent critical point result for differentiable functionals is exploited, in order to prove the existence of a determined open interval of positive eigenvalues for which the considered problem admits at least one non-trivial weak solution. Moreover, as a consequence of our approach, a multiplicity result is presented, requiring the validity of the Ambrosetti–Rabinowitz hypothesis. Successively, the Cerami compactness condition is studied in order to obtain a similar multiplicity theorem in superlinear cases. Finally, applications to Emden-Fowler type equations are presented. 相似文献
19.
Homoclinic orbits and chaos in discretized perturbed NLS systems: Part I. Homoclinic orbits 总被引:2,自引:0,他引:2
Summary The existence of homocliic orbits, for a finite-difference discretized form of a damped and driven perturbation of the focusing
nonlinear Schroedinger equation under even periodic boundary conditions, is established. More specifically, for external parameters
on a codimension 1 submanifold, the existence of homoclinic orbits is established through an argument which combines Melnikov
analysis with a geometric singular perturbation theory and a purely geometric argument (called the “second measurement” in
the paper). The geometric singular perturbation theory deals with persistence of invariant manifolds and fibration of the
persistent invariant manifolds. The approximate location of the codimension 1 submanifold of parameters is calculated. (This
is the material in Part I.) Then, in a neighborhood of these homoclinic orbits, the existence of “Smale horseshoes” and the
corresponding symbolic dynamics are established in Part II [21]. 相似文献
20.
Summary
In this paper existence and multiplicity results for lightlike geodesics joining a point with a timelike curve on a class of Lorentzian manifolds are proved under intrinsic assumptions. Such results are obtained using an extension to Lorentzian Geometry of the classical Fermat principle in optics. The results are proved using critical point theory on infinite dimensional manifolds. An application to the gravitational lens effect is presented. 相似文献