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  • 1. Clapp, Mónica
    et al.
    Szulkin, Andrzej
    Stockholm University, Faculty of Science, Department of Mathematics.
    A simple variational approach to weakly coupled competitive elliptic systems2019In: NoDEA. Nonlinear differential equations and applications (Printed ed.), ISSN 1021-9722, E-ISSN 1420-9004, Vol. 26, no 4, article id 26Article in journal (Refereed)
    Abstract [en]

    The main purpose of this paper is to exhibit a simple variational setting for finding fully nontrivial solutions to the weakly coupled elliptic system (1.1). We show that such solutions correspond to critical points of a $\mathcal{C}^1$-functional $\Psi:\mathcal{U}\to\mathbb{R}$ defined in an open subset $\mathcal{U}$ of the product $\mathcal{T}:=S_1\times\cdots\times S_M$ of unit spheres $S_i$ in an appropriate Sobolev space. We use our abstract setting to extend and complement some known results for the system (1.1).

  • 2.
    Clapp, Mónica
    et al.
    Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico.
    Szulkin, Andrzej
    Stockholm University, Faculty of Science, Department of Mathematics.
    Multiple solutions to a nonlinear Schrödinger equation with Aharonov-Bohm magnetic potential2010In: NoDEA. Nonlinear differential equations and applications (Printed ed.), ISSN 1021-9722, E-ISSN 1420-9004, Vol. 17, no 2, p. 229-248Article in journal (Refereed)
  • 3.
    Lasiecka, Irena
    et al.
    University of Virginia, Department of Mathematics.
    Maad, Sara
    Stockholm University, Faculty of Science, Department of Mathematics.
    Sasane, Amol
    London School of Economics, Department of Mathematics.
    Existence and exponential decay of solutions to a quasilinear thermoelastic plate system2008In: NoDEA. Nonlinear differential equations and applications (Printed ed.), ISSN 1021-9722, E-ISSN 1420-9004, Vol. 15, no 6, p. 689-715Article in journal (Refereed)
    Abstract [en]

    We consider a quasilinear PDE system which models nonlinear vibrations of a thermoelastic plate defined on a bounded domain in , n ≤ 3. Existence of finite energy solutions describing the dynamics of a nonlinear thermoelastic plate is established. In addition asymptotic long time behavior of weak solutions is discussed. It is shown that finite energy solutions decay exponentially to zero with the rate depending only on the (finite energy) size of initial conditions. The proofs are based on methods of weak compactness along with nonlocal partial differential operator multipliers which supply the sought after “recovery” inequalities. Regularity of solutions is also discussed by exploiting the underlying analyticity of the linearized semigroup along with a related maximal parabolic regularity.

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