• Nonlinear equations with natural growth terms 

    Jaye, Benjamin James (University of Missouri--Columbia, 2011)
    This thesis concerns the study of a class of second order quasilinear elliptic differential operators. For 1 < p < ∞, the model equation we consider is: (1) L(u) = -Δpu - σ∣u∣p-2u. Here the potential is a function (or ...
  • Potential theory and harmonic analysis methods for quasilinear and Hessian equations 

    Nguyen, Phuc Cong, 1976- (University of Missouri--Columbia, 2006)
    The existence problem is solved, and global pointwise estimates of solutions are obtained for quasilinear and Hessian equations of Lane-Emden type, including the following two model problems:-[delta]pu = uq + [mu], Fk[-u] ...
  • Potential theory methods for some nonlinear elliptic equations 

    Seesanea, Adisak (University of Missouri--Columbia, 2018)
    This dissertation presents a unified approach via potential theory for solvability of a class of nonlinear elliptic equations.
  • Quasilinear elliptic equations with sub-natural growth and nonlinar potentials 

    Cao, Dat Tien (University of Missouri--Columbia, 2015)
    Necessary and sufficient conditions for the existence of finite energy and weak solutions are given. Sharp global pointwise estimates of solutions are obtained as well. We also discuss the uniqueness and regularity properties ...
  • A sublinear version of the Schur test and weighted norm inequalities / 

    Quinn, Stephen (Stephen Michael) (University of Missouri--Columbia, 2017)
    In this dissertation, we provide results which characterize when a class of partial differential equations can be solved. These partial differential equations arise in the study of the Porous Media Equation, which can model ...