Vicentiu D. Radulescu - profile picture on SciLag

Vicentiu D. Radulescu

  • Analysis of PDEs
  • General Mathematics
  • Classical Analysis and ODEs
  • Mathematical Physics
  • ArticleNonhomogeneous quasilinear elliptic problems: linear and sublinear cases

    Journal d'Analyse Mathématique (accepted)

    • mountain pass solution
    • Palais-Smale condition
    • non-homogeneous differential operator

    Posted by: Vicentiu D. Radulescu

    arXivfulltextMSC 2010: 35J60 35J62 58E05

    We are concerned with a class of second order quasilinear elliptic equations driven by a nonhomogeneous differential operator introduced by C.A. Stuart and whose study is motivated by models in Nonlinear Optics. We establish sufficient conditions for the existence of at least one or two non-negative solutions. Our analysis considers the cases when the reaction has either a sublinear or a linear growth. In the sublinear case, we also prove a nonexistence property. The proofs combine energy estimates and variational methods. In particular, the monotonicity trick is applied in order to overcome the lack of a priori bounds on the Palais-Smale sequences.

  • BookNonlinear Analysis - Theory and Methods

    Springer, 2019

    • nonlinear analysis
    • elliptic equation

    Posted by: Vicentiu D. Radulescu

    fulltextMSC 2010: 35J60 35-02

    This book emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The content is developed over six chapters, providing a thorough introduction to the techniques used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations as well as their applications to various processes arising in the applied sciences. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book a nice balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis.