Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations

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Focusing on the dynamical system approach, this book systematically explores the symmetrization and stabilization of nonnegative solutions to nonlinear elliptic problems in asymptotically symmetric unbounded domains. It introduces innovative methods, including trajectory dynamical systems and new Liouville-type results, to analyze elliptic equations. By leveraging symmetry and monotonicity, the author characterizes the asymptotic behavior of solutions and contrasts traditional elliptic partial differential equations with dynamical systems methods, offering valuable insights for mathematical biologists.