Joanna Janczewska - Publications - Bridge of Knowledge

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  • Subharmonic solutions for a class of Lagrangian systems

    We prove that second order Hamiltonian systems with a potential of class C1, periodic in time and superquadratic at infinity with respect to the space variable have subharmonic solutions. Our intention is to generalise a result on subharmonics for Hamiltonian systems with a potential satisfying the global Ambrosetti-Rabinowitz condition from [P. H. Rabinowitz, Proc. Roy. Soc. Edinburgh Sect. A, 114 (1990), 33-38]. Indeed, we weaken...

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  • The Maslov index and the spectral flow—revisited
    Publication

    We give an elementary proof of a celebrated theorem of Cappell, Lee and Miller which relates the Maslov index of a pair of paths of Lagrangian subspaces to the spectral flow of an associated path of self-adjoint first-order operators. We particularly pay attention to the continuity of the latter path of operators, where we consider the gap-metric on the set of all closed operators on a Hilbert space. Finally, we obtain from Cappell,...

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Year 2018
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Year 2015
  • Homoclinic and Heteroclinic Orbits for a Class of Singular Planar Newtonian Systems
    Publication

    - Year 2015

    The study of existence and multiplicity of solutions of differential equations possessing a variational nature is a problem of great meaning since most of them derives from mechanics and physics. In particular, this relates to Hamiltonian systems including Newtonian ones. During the past thirty years there has been a great deal of progress in the use of variational methods to find periodic, homoclinic and heteroclinic solutions...

  • On Von Karman Equations and the Buckling of a Thin Circular Elastic Plate

    We shall be concerned with the buckling of a thin circular elastic plate simply supported along a boundary, subjected to a radial compressive load uniformly distributed along its boundary. One of the main engineering concerns is to reduce deformations of plate structures. It is well known that von Karman equations provide an established model that describes nonlinear deformations of elastic plates. Our approach to study plate deformations...

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  • Subcritical bifurcation of free elastic shell of biological cluster

    In this paper we will investigate symmetry-breaking bifurcation of equilibrium forms of biological cluster. A biological cluster is a two-dimensional analogue of a gas balloon. The cluster boundary is connected with its kernel by elastic links. The inside part is filled with compressed gas or fluid. Equilibrium forms of biological cluster can be found as solutions of a certain second order ordinary functional-differential equation...

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