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  • Dispersion relation for water waves with non-constant vorticity 

    We derive the dispersion relation for linearized small-amplitude gravity waves for various choices of non-constant vorticity. To the best of our knowledge, this relation is only known explicitly in the case of constant ...
  • Existence of ground states for fourth-order wave equations 

    KARAGEORGIS, PASCHALIS (Elsevier, 2010)
    Focusing on the fourth-order wave equation utt+?2u+f(u)=0, we prove the existence of ground state solutions u=u(x+ct) for an optimal range of speeds and a variety of nonlinearities f.
  • Supercritical biharmonic equations with power-type nonlinearity 

    We study two different versions of a supercritical biharmonic equation with a power-type nonlinearity. First, we focus on the equation Delta(2)u = vertical bar u vertical bar(p-1)u over the whole space R(n), where n > 4 ...